Nuclear fission was discovered in 1938. The previous concepts of "atomic bombs" were not fission-based. Rather, they tended to be based (per H.G. Wells) on the idea of induced radioactivity. That is, the idea that you could release the energy from radioactive materials all at once, rather than waiting for it to decay.

That's if the mechanism was spelled out. Usually only the effects were spelled out: e.g., in Wells' book, he talks about the atomic bomb as creating fires that could not be put out and continually grew. He only gestured at the idea of how they might work.

H.G. Wells is generally considered the originator of the trope of atomic bombs, in his 1914 novel The World Set Free. It was itself largely influenced by Frederick Soddy's work of popular science, The Interpretation of Radium (1909) which discussed the immense amount of power locked up in atoms. Soddy's work was directly influenced by Soddy's own (Nobel Prize-winning) research with Ernest Rutherford on atomic transmutation.

I don't think I've seen the concept of atomic bombs even hinted at prior to 1914 (it is not in Soddy's book; Soddy originates many other "atomic energy" tropes though, like the "one pound of uranium could power a steamship to go around the world X number of times" one). By the 1920s however it was very commonplace and you could find it in many works of science fiction, popular science, science journalism, etc.

A great resource for the history of thinking about nuclear technology is Spencer Weart's Nuclear Fear, which traces a lot of these early threads back.