The first post-WWII non-victory war was Korea. It started during Truman’s administration, and that administration was a generation older than the WWII vets.
I wasn’t measuring it by who was President and the oldest of the political leadership, by the way WWII could be called the greatest stalemate of all, it was the resulting unfinished war with the German/Soviet alliance that led to decades of stalemate and defeats under weak leadership.
The fighters of WWII were already covering a wide range of ages by the early fifties, roughly age 23 to 45 let’s say, they were already having a heavy influence on leadership and politics. Vietnam and 1960s/1970s America was all theirs to run, and they ran it into the ground.