There were a bunch of things that came together perfectly.
1) A bunch of intellectuals of the higher caliber that could be brought into a single location. A lot of this had to do with the rise of Nazism which led to a lot of these high powered intellectuals fleeing Germany and Eastern Europe for the US.
2) A bunch of money that could be poured into the project. At that time, the USA was completely committed to using every resource it had to win WWII.
3) Convince all those intellectuals that working on creating the most destructive weapon ever was a good thing. If there was ever a "good war" in the history of the world, it was the war against Hitler. I think almost everyone in the West understood at that time that stopping Hitler was of the highest moral imperative and that massive amounts of violence was the only way to stop him. Even with all this, people like Oppenheimer had their doubts. (Of course this would end up being used, not against Hitler and the Germans but against the Japanese).
4) The theoretic foundations for all this work were just laid a few decades before. This could not have happened before then.
I don't see such a convergence of factors happening afterward. I don't think you could get the top 100 leading scientists together to build a superweapon now.
If it were not for the Manhattan Project, I think it is likely that we would still be living in a nuclear weapon free world. Though, if that is a good thing or a bad thing with respect to great power wars, I am uncertain.