I think the earlier the better, since India had about a century of Chaos between the death of Harsha in 647 and Lalitaditya/Yashovarman around 750.
But this would mean deemphasizing the Byzantine wars by sending the 100k troops of 717 siege of Constantinople to India instead.
OTL, the Caliphate's governor of Eastern Arabia first started raiding the Indian coasts, as far as Thane in the 630s. But Umar ibn alKhattab stopped them, due to his dislike of Naval campaigns.
In 644 the Battle of Rasil occurred, on the Hub river close to modern Karachi. But the army sent back a report that Makran was extremely desolate and barren and for some reason, they said Sindh was even worse. This misinformation prevented them from pressing on to Sindh proper.
Thereafter, Qusdar/Khuzdar, a city controlling the Bolan mountain pass between Sistan and Sindh was taken in the reign of Muawiyah, but no campaigns save small reconnaissance missions were sent to Sindh.
Instead, the Caliphate was much more focused on the much poorer and far more difficult invasion of Zabulistan and Kabul, which resulted in repeated and humiliating failure and losses of thousands of men.
Until finally in 711 alHajjaj sent a proper campaign under Muhammad alQasim, with a relatively small force of 15,000. After 2 years taking Sindh, with further campaigns deep into Punjab, reaching the Himalayan foothills. Bringing in a staggering 600 million dirhams.
A decade later, a new governor, Junayd alMurri greatly expanded Muslim domains, taking Rajasthan, most of Gujarat, some of Haryana and pushing into Madhya Pradesh. Bringing in 400 million dirhams.
But he left for Khurasan, his replacement Tamim lost all his gains and even lost Sindh itself. So a new replacement was sent, Hakam ibn Awana who retook Sindh, established Mansura/Brahmanabad and reconquered Junayd's conquest until 738 at the Battle of Navsari near the Maharashtra border, with the newly emerging Pratihara empire, where he lost, partly due to manpower shortages. Subsequently all his conquests were again lost, and even Sindh was threatened. After that, the abbasids took over, who no longer had expansionist zeal, and Muslim expansion stopped for 300 years until the Ghaznavids.
The Conquest:
So PoD would be that in 644 the expedition in Rasil reports about the immense wealth of Sindh and India beyond it. So that the Caliphate recognises that it is the richest of all its frontiers by far, and so should receive manpower and resources equivalent to its riches.
Thus, no attempt are made on Zabulistan/Kabul, Sistan being entirely defensive.
Similarly the strange offensive policy of attempting to raid the Khazar steppe would also be prevented. Instead establishing defensive garrisons at Derbent and Tbilisi/Darial to prevent Khazar incursions, but never going on the offensive, since nothing is gained.
In Central Asia expanding to Khwarezm and Chaghaniyan/Tokharistan. But adopting a more defensive approach to Sogdia due to the Turgesh Turks.
Against the Romans, being less brazenly offensive, instead of raids deep into Anatolia, where logistics are stretched and the army is vulnerable, attempting the much slower gradual annexation of fortress by fortress and city by city. Slowly pushing the frontier and creating bases of operations on the Anatolian plateau, making logistics far better. But this would be slow and more costly.
In the west, integrating the Berbers much better to allow even greater reliance on them, improving the manpower situation. And attempting gradual conquest of Sicily instead of 20 years of useless raids.
This far more defensive approach means far more troops are available for Indian campaigns.
After the Battle of Rasil, the Caliphate is still campaigning in eastern Iran against Sassanian remnants and rebellions. But as they die down, in 650 the Persian Gulf navy would take the coastal city of Daybul.
After the death of Yazdgerd in 651, around 10k men would be sent to Daybul, giving 15k in total. Who would then defeat the dynasty and take the capital by 653 and beginning to push towards Lahore. While tens of thousands of Bedouin, predominantly from eastern Arabia would begin to be transferred to the Thar desert, defeating the proto Rajput pastoralist nomads of the region. The completion of the Khurasani campaign in 654 would give further reinforcements. Marching on Thanesar in Haryana, the second capital of Harsha's recently disintegrated empire, taking it in 655 without too much resistance.
Finally in 656 taking Kannauj, the capital of all north India, probably without too much difficulty due to Harsha collapse. The riches of the city bringing in immense wealth to the Caliphate. In total the India campaign would probably bring in over a Billion Dirhams, bankrolling the rest of the Caliphate.
With Kannauj, the small statelets and chieftains of Bihar/Bengal and Madhya Pradesh are vulnerable, perhaps voluntarily submitting to Muslim controlled Kannauj. But by early 657 the assassination of Uthman and first fitnah would've reached the troops at Kannauj. Preventing any further campaigns and forcing them to go on the defensive for the next 4 years.
Polities in Bihar and Madhya Pradesh might be able to form a coalition and take advantage of Muslim weaknes perhaps pushing all the way to Kannauj and even besieging the city. But the instability of the coalition would eventually break the siege allowing the Muslim garrison to hold out. While in the Indus valley, the Turk Shahi of Peshawar would probably take much of Punjab up to Multan, reducing them to Sindh.
This precarious position would be ended after the end of the fitnah in 661, whereupon Muawiyah wouldn't focus on the Byzantines anywhere near as much as OTL, due to the Billions of dirhams obtained from India.
Sending around 35-40,000 troops to Sindh, to retake Punjab, and reinforce Kannauj. (OTL 50k were sent to Khurasan in 670) In total by 664 India would have around 60k-65k troops, around a third-quarter of the Caliphate's total manpower. Kannauj taking Bihar/ Western Bengal and Madhya Pradesh by 667. While Sindh takes Gujarat with help from the Gulf navy on the coasts at the same time. Ideally capturing the brilliant mathematicians Brahmagupta and Bhaskara i, moving them to Iraq where their mathematical works and Hindu numerals would be translated and adopted over a century earlier.
Beginning the Deccan campaigns, dominated by the Chalukyas of Badami under Vikramaditya I though contested by the Pallavas of Andhra Pradesh, who had recently occupied their capital for 13 years from 642 to 655. The Thar Bedouin would've already begun to push into the arid savanna of the western Deccan in the mid 660s. In 669 a more organised campaign would begin, the Sindhi/Gujarat army focusing on the western Deccan, while their navy attacks the Konkan coast. And Kannauj would focus more on central and western Deccan, assisted by the emerging Bengal navy. Perhaps Making an Alliance with Parameswaravarman of the Pallavas against the Chalukya.
Thus in 674, the Battle of Peruvalanallur (Tiruchirappalli) which OTL was a victory for the Pallavas despite being greatly outnumbered, would be much more divisive with the Caliphate's assistance. Probably slaying Vikramaditya I on the field. Thereafter Badami would be besieged, falling quite quickly due to the massive loss at Peruvalanallur. With its capture, the rest of the Chalukya realm would fall by 675. While the Pallavas would annex the eastern Chalukyas.
Though Badami is a little too southerly for Kannauj/Sindh to maintain. So a new Deccan capital might be founded further north near Aurangabad, since it's closer to the Muslim heartlands within India and is close to the coastal trading centre of Thane/Mumbai.
For now, the Pallavas would be left alone for their assistance against the Chalukya. Instead pushing south against the western Gangas and finally the Pandaya of Madurai.
After a decade, by 680 at Muawiyah's death, almost all the Deccan would've fallen. The many Billions of dirhams brought into by the Indian would probably make the Umayyads shift from isolated Damascus to Iraq, perhaps even Basra - the closest city in the fertile crescent to India, which would make the second fitnah a completely different story. Since Muawiyah would less focused on the Romans, Yazid may be sent to India instead, which would also have major ramifications on the 2nd fitnah, as would the east Arabian Bedouin migrations - perhaps preventing or significantly reducing the Najdat khawarij
But butterflies to the 2nd fitnah are difficult to predict. So I'm just assuming it'll happen similar to OTL. During the decade long civil war, rebellions would spring up all over India. The most significant of which led by the Pallavas in southern India, taking advantage of the civil war to rally former Chalukya nobles to its cause taking Badami and most of the Deccan for itself. But the more consolidated Indo-Gangetic's rebellions would be successfully put down.
After the civil war has ended, in 692 tens of thousands would be sent to reconquer the Deccan, including ibn alAshath and his peacock army. Giving over 100,000 troops in the whole of India. Taking Badami back in 694, then marching on the Pallava capital Kanchipuram, taking it in 696. Ending the last major independent state in India.
From there, strengthening the Gujarati/Kokan and Bengali navies to take the Malabar coastal cities and strengthen control over the Coromandel coast. Even establishing Muslim control over bits of coastal Sri Lanka. By the year 700. After 56 years of campaigns since the Battle of Rasil, India would be conquered. (Save for the mountainous and densely forested region of Odisha/ChotaNagpur - later perhaps being a base for Alid revolts against the Caliphate )
Development
The Caliphate can now focus on developing India.
At the time, much of India was still covered in vast, dense forest or in other regions dominated by Pastoralists.
The Gupta empire had set in motion the first inklings of agricultural expansion, but it wouldn't take off until their medieval successor dynasties like the Pratihara empire or Pala empire in the seventh to tenth centuries.
ITTL, a unified and more centralised India would be able to carry out irrigation projects on much grander scales. Especially as Islamic law heavily incentivizes bringing barren land into cultivation, by halfing the tax rate. Resulting in huge Arab and Muslim migrations, as well as large population increases all throughout the subcontinent over the next century, With Kannauj reaching over 1 million people and rivaling Chang'an for position of the greatest city on earth.
After the campaigns are over the Bengali and Gujarati navies would be redesigned for a greater emphasis on trade, particularly the lucrative eastern trade with the Tang Dynasty and spice islands. Soon dominated by Muslims.
Perhaps establishing a land connection with the Tang Dynasty from navigable Dibrugarh in Assam through the mountains of the kingdom of Nanzhao (Yunnan) until reaching Chengdu in Sichuan. Which would increase contact between the Indian and Chinese worlds. Ideally in advancements of rice cultivation and the highly developed 3 departments and 6 ministries system of Chinese administration. With Indian influences in Yunnan, Sichuan and Guizhou, as well as Chinese influences in Assam and Bengal. Though the difficulty of the terrain may make the route unfeasible...
In South East Asia, Islam would begin to emerge in the ports cities, as Indian Ocean trade increases in volume. Challenging the Hinduism and Buddhism of the region, which were still in fairly early stages in the region. Eventually a Chola style invasion could occur, thus the Caliphate itself extending all the way to SEA. Though the region was still dominated by thick rainforests, with major agricultural expansion not occuring until the mid-late medieval period. So the Caliphate would be able to greatly speed this process, making SEA much more prosperous, populous and thereby far more influential on a world stage centuries earlier.
Due to the sheer distances, most connection between India and the middle east would be done by the navy. Particularly the Hajj, with Jeddah becoming a large port much sooner. Similarly, Yemen being much more important than OTL due to its strategic location on the maritime routes. Also extending to Ethiopia with the remnants of Axum and the emerging Harla kingdom and Shewa Sultanate.
The riches of India, the agricultural expansion and trade would encourage massive Arab settlement throughout India, including many Umayyad princes.
With many of its cities surpassing Kufa and Basra as the intellectual centres of Islam. With these Indian cities producing Madhabs, qira'aat, schools of grammar, hadeeth narrators, poets, geographers, historians, scientists etc, throughout the 8th century. Thus not only being the economic heart, but also the intellectual heart of the entire Muslim world. With students from across the Muslim world travelling to study in India. (Basically TTL's India is equivalent to OTL Iraq+Persia)
ITTL, Persia's impact on the Muslim world would be significantly less than OTL.
Potentially, the earlier islamification of SEA and its proximity of the intellectual behemoth of India, would mean it's Muslim scholars are far more influential on Islam as a whole, with works written by them being studied throughout the Muslim world.
Similarly, greater Indian Ocean trade dominated by Muslims would mean more Muslim settlement in Guangzhou, Yangzhou and other ports of China. Perhaps even venturing as far as Korea and Japan. While in the west, earlier and more extensive Muslim settlement along the Swahili coast - being a much more influential part of the Muslim world due to that.
Soon, the Indian Ocean would become a Muslim lake, centred on Caliphal India.
The West:
Meanwhile, in the west, campaigns would be undertaken mostly for strategic reasons - to protect the Egypt and Levant from Mediterranean invasions, since any wealth gained from the conquest of the Maghreb or Iberia would be trivial compared to the immense wealth of India. Said wealth would be used to make the conquests easier, paying off and bribing nobles and influentials to willingly join the side of the Caliphate. Such as the Soghdian merchants, Armenian/Anatolian lords, Berber chiefs or Khans of the steppes etc.
Due to the majority of Arab manpower being tied up in distant India, the western campaigns would be even more dominated by Berbers than OTL, with the increased wealth allowing the equipment and training of far more Berbers, giving much more manpower in the west (OTL Berber revolt 300,000 are said to have fought against the Arabs, but most didn't have armour or weapons). This heavy dependence on the berbers would mean the Umayyads would need to treat them much better, the Caliphate's increased wealth would allow them to pay the Berbers much higher salaries, ideally preventing revolt.
But on the whole, without significant Arab settlement in the west and the focus on India Caliphate would neglect the west even more than OTL, soon slipping away into an independent Berber empire, stretching from Tripoli to the Pyrenees, though nominally loyal to the Caliphate. Basically alMohads but 400 years earlier.
The lack of the 740 Berber revolt, would mean Alfonso I is unable to take advantage of the chaos to expand into Galicia and upper Duero valley (regions primarily garrisoned by Berbers who left their posts in the revolt). And Iberia would be probably be more stable, since there isn't a small Arab ruling class dominating the Berber (later Muwallad) Muslim majority. Similarly, Iberia would be permanently attached to the Maghreb unlike OTL during the 350 year gap between the Berber revolt and the AlMoravids. Which caused tensions between the Andalusis and the Berbers, a factor in the Berber sack of Cordoba in 1013.
The lack of the revolt, greater stability/cohesion and increased manpower due to the Maghreb means that Septimania wouldn't fall to the Franks in the 750s. This would mean the Franks would be the main enemy, not Asturias, with almost annual summer raids against the Franks, and control over Gijon and the Asturias coast means Andalusi pirates in the Atlantic. Thus Andalus would have far more direct contact and impact/influence with western and northern Europe than OTL.
In the reign of Charlemagne Andalus would likely be put on the defensive, perhaps temporarily losing Septimania, though probably able to hold the line at the Pyrenees passes, preventing Iberian incursions. But with accession of the weaker Louis the Pious, they would be able to go on the offensive once more. As Frankia gets weaker and weaker over the decades, having greater success. By the late 800s, with the Vikings terrorising the north, and the state collapsing, Andalus would probably annex most of Aquitaine and the Rhine valley. Greatly changing Western European history. Assuming France regains it's strength, they would be a gradual reconquista, pushing the Muslims back to the Pyrenees. But by this time, Iberia would be quite thoroughly islamicizied. (Faster than OTL due to continuous Berber migrations from Maghreb). So there would be no reconquista of Iberia.
Similarly without the Berber revolt Sicily may be conquered earlier. Ideally, they would attempt the gradual conquest on their first landing on the island in 704. But if not, then after 30 years of raiding, in 740, Habib ibn Abi Ubayda al-Fihri finally led a campaign to conquer the island. But was prevented from doing so by the Berber revolt. ITTL, without the revolt that conquest could occur. Unlike the Aghlabid conquest in the mid 800s, the Byzantines are much weaker, still reeling from the Islamic conquests, perhaps allowing more lasting conquests in Apulia and Calabria.
With Sicily, the Berbers would control the entire western Mediterranean. With Caliphal attention they could extend further east, to Cyrenaica and perhaps the Berbers of the Siwa oasis near Egypt. OTL Andalusi pirates took Alexandria in the 820s and then Crete, so this could be possible ITTL, extending Berber power deep into the eastern Med as well...
Due to the heartland of Islam being in India, many Berber students would travel the immense distance, halfway across the world to study in the great intellectual centres of India, bringing this knowledge back to the west. Due to their annexation of southern France, western Europe would be directly impacted by Indians far more than OTL. Perhaps a few Christians or Jews of Southern France travelling through the Pax Islamica all the way to India.
The decline of the middle east:
With the climatic catastrophe of 920-1070 throughout the middle east, there would be mass migration of middle easterners to the unaffected regions of India as well as SEA, further increasing those region's islamification. While the middle east would be somewhat abandoned.
The Turkic nomads taking over Khurasan, northern Persia, Caucasia and Anatolia, desperately searching for pastures due to climatic problems in the steppe. With the Berbers in the west, taking over much Egypt and the Levant, able to supply them with Ifriqiyan and Sicilian grain in wake of the Eastern Mediterranean drought - as Fatimids did OTL, but this time controlling the majority of the entire Mediterranean.
The Caliphate definitively relocating to India due to Baghdad literally freezing over, even snowing in Basra....
Though it's navy would use the navigability of the Tigris-Euphrates to maintain some control over Iraq, preventing the nomads from completely ravaging it and the Persian gulf ports to protect Fars and southern Persia. Similarly in Egypt the Berbers would initially still be nominally loyal to the Caliph, with the port of Suez/Clysma still under Caliphal control, perhaps sending Indian grain barges to help when the Egyptian situation reaches its worst levels in the early-mid 1000s.
By the time the climatic troubles end in 1060-1070, agriculture would've drastically declined throughout most of northern Persia, replaced by nomadism. While the Berbers would've firmly unified much of the Mediterranean under their empire no longer nominally loyal anymore, perhaps with their own Caliph due to the distance of the Indian Caliph, but probably not actively hostile. The Indian Caliph would still have some influence over Egypt due to the important Indian grain barges and the economic benefits of its IO trade.
The Indian based caliphate would use the return to climatic normalcy to revitalise the agricultural systems of Iraq. Using Iraq and southern to gradually exert control over the nomads of the north. Though, if the Mongol invasions still occur, then another round of mass migration to India would happen....
But Iraq would largely be a distant frontier on the edge of the Caliphate. It's attentions more focused on the agricultural, demographic and economic expansion of SEA, gaining a boost via the migration of hundreds of thousands of middle eastern refugees.
Perhaps, during the 5 Dynasties 10 kingdoms period, the Caliphate attempting to exert direct influence over the Chinese coasts. Initially helping the Vietnamese in the Battle of Bạch Đằng. Then supporting/vassalizing the kingdoms of the southern Chinese coasts: Southern Han, Wuyue and Min via the formidable Caliphal navy operating out of ports on Taiwan and Luzon. Investing in their shipyards and fleets, using them to raid the northern Chinese coast, perhaps even raiding up the Yellow and Yangtze rivers.
While on land supporting the Great Shu of Sichuan, via Yunnan, which would be vassalized in the wake of Nanzhao collapse.
Leading to a naval arms race between the southern Chinese supported by the Caliphate and Song Dynasty of the northern plain.
Though I'm not knowledgeable enough in Chinese history to know the effects of this...
Overall, the Muslim world would be split by the Mediterranean based Berber Caliphate and the eastern Indian Ocean Caliphate.
