Given the amount of forces Athens brought to bear and the sheer lack of organization the sources describe on the Syracusan part before the arrival of the Spartan commander, I do believe a more dynamic approach led by Alcibiades might well have worked. But I don't see them doing a straight up attack on Syracuse, they require a base closer, so I see the capture of Catane taking place, and from there an attack on Syracuse that would be led more efficiently. Even if Lamachos dies then Alcibiade remains, completing the fortifications and making sure the fleet is more active, potentially capturing the 4 ships of Gyllipus. The siege itself would take some time, the city is large and well fortified, but the constant reinforcement of the walls around it prevent any sortie by the Syracusans while the fleet keeps the harbor mostly shut. We are in a time before catapults or other siege weapons of the kind, the only solutions are primitive rams that are massively inneficient. Instead of wasting too much time, Alcibiade may organize expeditions rotating soldiers to coerce the rest of Sicily into supporting him. His mastery of the sea negates any advantage in cavalry the enemy might have, and he manages to subdue enough cities to actually cover his costs and keep his army in the field. After a full winter that does not see the Athenians go back home the Syracusans are forced to admit their defeat and submit to Athens. Their fleet is seized, and a guarrison is installed on Ortygia before most of the Athenians go back home. The expected plunder did not materialize, but enough come back home somewhat richer than they left for the expedition to be deemed a success. On the way back the Athenians stop in Corcyra and then on the nearby mainland, enforcing their will on the Corinthian colonies who don't dare fight the heroes of Sicily, especially as Corinth does not feel it can beat the Athenian fleet.
The return in Athens is a triumph, and Alcibiade is elected strategos for the third year in a row.