The way I like to talk about this is in this way: what are the phases necessary for developing a nuclear weapon? In some ways, it’s easiest to first talk about this in the context of the American Manhattan Project.
In 1939, Einstein and Szilard wrote the famous letter to Roosevelt about bomb issues. FDR said, “sounds interesting,” and made a very small exploratory committee to look into it (the Uranium Committee at the National Bureau of Standards). This is what we might call an exploratory stage. It was basically theoretical studies and small laboratory studies. The questions they were trying to answer were very basic: Is atomic energy something worth worrying about? Can an atomic bomb, or an atomic reactor, be built in the near term by anybody?
The conclusions they came to weren’t encouraging. By 1941 the top science advisors in the US had basically concluded that while it might be possible to make nuclear weapons, it was going to be very difficult to do so and probably not worth spending a lot of money and time on in the near term. The atomic bomb, they reasoned, was unlikely to play a role in World War II.
Towards the end of 1941, though, they received a report from scientists working in a similarly exploratory capacity in the UK which concluded that the bomb could probably be built in a short amount of time if a sufficient effort was put into it. The British scientists were successful in convincing the American administrators that the program should be moved into a new stage of development.
This new stage we might call the pilot stage. It sought to establish on a small scale some of the key aspects that would go into a real production model. Roosevelt approved this just before Pearl Harbor. Basically this required building several small-scale production plants, and funding work on building an experimental nuclear reactor.
By mid-1942 it became clear that they felt this was all worth spending more money on, and by late 1942 it was decided that the US Army should be brought into the matter, because they had the experience necessary to construct the massive factories and plants necessary to produce actual atomic bombs. This is the transition into the production phase. You’ll note that in this case, the pilot stage was very brief. This was unusual and noted even at the time; they were really flying by the seat of their pants, drawing up plans to build full-scale industrial reactors even before the first experimental nuclear reactor had gone online (which happened in December 1942).
It is this final phase, from 1943 to 1945, that is the Manhattan Project proper, when it was run by the Manhattan Engineer District of the US Army Corps of Engineers. This is the full (crash) production program to make atomic bombs, and required a huge expenditure of resources.
There is some irony in the fact that the original, 1941 estimate by the US scientists about the difficulty of making an atomic bomb was more or less correct. They had concluded that a bomb, though feasible, would be very difficult to make, and that nobody else was likely to really be working on one. The UK scientists underestimated the difficulty substantially. The final bomb project cost about 5X what was estimated in 1942, when it started the transition into the production phase, to give some indication of the disparity of estimates. And we now know, of course, that making an atomic bomb was difficult and no other nation did get very far in it during the war.
OK, but back to Germany. Where did they end up? They started their exploratory phase in 1939, the same as the USA (and the same as the USSR, Japan, France, and the UK). Like the US, they concluded that this was interesting but pretty difficult. Nobody thought this was going to be an issue in the present war — which, of course, Germany was doing very well in, early on.
By 1942, they started to realize that things weren’t going so well. They started to get more interested in the uranium issue. But even then, it was still just a transition towards the pilot stage — they were looking into building an experimental reactor. They were hampered in this by many factors.
They never got to the end of this phase before the war ended. What if they had? They still would have to start a production phase, which was the most difficult and most costly of the phases.
So by 1945 they were almost to the phase that the United States moved out of in 1942. They were pretty far from getting a bomb, and even if they had decided, in 1942, to start building one, it’s really unclear that they would have been able to pull it off, merely because the sizes of the buildings required for such a program would make them very attractive bombing targets.