Till July, 1945 not a person in the world knew whether the nuke would actually work. It would have been the height of irresponsibility to build a war strategy based entirely on the success of an experimental weapons program.
Not to mention that with no Allied troops on the ground in Europe there would have been nothing to stop the Red Army from going to the Channel.
While we had nukes by mid-1945, we had very few nukes.
Once they had nuclear fission proved, they had nukes if they wanted them ~ and that happened on December 2, 1942 at Alonzo Field Stagg Stadium in Chicago!