Honestly, the best winning move in regards to Vietnam is to simply not play. President Johnson should have pursued a strategy similar to the Eisenhower administration in addition to a more successful “Vietnamization” strategy. Both of these should result in the South staying strong up until the end of the Cold War - when the two Vietnams either reunify or the North goes full Kim mode and China uses it like a buffer state.
Without focus on the Vietnam War, it’s possible that President Johnson would’ve used all that government money to be used in the Great Society programs and Space Race. This could cause either one of them to be more successful than OTL. Also, even without Vietnam, there would still be something like the hippie movement as a backlash to the social conformity of the 50s. However, these alternate hippies could be less militant and revolutionary, and more practical and peaceful. A lot of the anti-war protestors could have also poured their energy into supporting the Civil Rights Movement, Environmentalism, Feminism, and Gay Rights instead.
TLDR: The Vietnam War and its consequences have been a disaster for the human race.