Inquisitive and imaginative scientists set the stage before the European War erupted.
Earlier discoveries concerning radioactive elements set the stage. Then...
While crossing a London street in 1933, Leo Szilard imagined the nuclear neutron chain reaction, the key to the atomic bomb/fission reactors. However he had no known material that would support a chain reaction.
In 1934, Leo Szilard was granted his patent on the chain reaction and the atomic bomb.
In 1936, Leo Szilard signed his patent over to the British Admiralty to keep it out of the hands of the Nazis in Germany.
In 1938, Otto Hahn in Berlin discovered that Uranium-235 fissioned when hit by a neutron and produced excess neutrons. This made Szilard's patent practical.
War/threat of war, accelerated the practical development, though.
If interested in the topic, the book "The Making of the Atomic Bomb", by Richard Rhodes, is a fascinating (to me) account of all the discoveries, theoretical, and practical work leading up to the bomb.
Thanks Ray! Interesting. Yes, it seems you're right that the discovery of the technology itself happened before the war. So it's the same history as with aviation then: The technology existed prior to WWI, but was greatly accelerated by the war.
Thanks for the tip about the book. I'll definitely have a look at it.