When the bombs were ultimately dropped, yes, but the Manhattan Project (actual development of the bomb) took place coinciding with the Nazi nuclear program before the defeat of Nazi Germany.
The Nazis actually started ahead of the Americans in 1939, and had the scientist who discovered nuclear fission as part of the program. The Nazis by all accounts had a head start and better scientists.
It wasn’t until it was clear the Nazis were using heavy water (i.e focusing on nuclear reactors) in 1942 that the US got the first clue that the Nazis had abandoned the idea of nuclear bombs in the war effort, but the project was still funded in Nazi Germany until the end of the war in 1945.