The first test bomb was detonated in July 1945. So indeed, there was no bomb in March 1945, but once they had a working model, there was no looking back. 1 month later the bombs were dropped on Japan. Most of the money spent on the project during the duration of the war was used to produce bomb grade material, they all knew a runaway reaction would release a lot of energy. The first nuclear reactor which proved the bomb would work was built in 1942 under a university stadium with a minimal amount of shielding. The problem was building the trigger, not the theory or procuring the fuel. In conditions where they were never under threat of attack and with all the money and all the people working on the project it was only a matter of time before they succeeded. Any time the Germans built anything like jets, drones, or missiles, that could change the outcome of the war, the allies blew it up. The Germans had to go to great lengths to build underground factories that were never completely immune from being blown up. Cut off from oil early in the war, the Germans got their petroleum products from synthetic fuel plants. It wasn't until early 1945 after a lot of bombing raids that the synthetic fuel plant output was cut to a fraction of what it was during the bulk of the war. While science can't do everything, if given enough time, it does seem capable of moving mountains.