Fermi, working through elements methodically to see what happened when they were ‘bombarded’ with neutrons, expected to make new isotopes, but in 1934 was puzzled by his results with uranium, and probably dismissed what he found as a contaminant. Only in 1939 did Hahn & Strassmann identify barium (and krypton?). Then Lise Meitner and Frisch provided the ‘liquid drop’ model of fission of nucleus into two parts.
Szilard noticed fission fragments must emit
Neutrons if they split; H G Wells's chain reaction idea, based on the ideas of Frederick Soddy (The Interpretation of Radium, 1907, revised later as The b2c datasets Interpretation of the Atom), in The World Set Free (1914), became a possibility [Clark]. Again, this was empirical—it was found that elements with high atomic numbers have proportionally more neutrons than low ones. Nobody had any idea why. But, clearly, if a heavy element split, there would be surplus neutrons.
Uranium-235 isotope fission was proved
To happen by experiment; it was guessed, and proved, that U235 was the portion of uranium which was most liable to fission. Nobody knew (or knows now) why it differed from U238, except perhaps in the sense that an odd number was expected to behave differently from an even number.
1939: Bohr and Wheeler at Princeton realised fast free neutrons were produced during fission. In 1939 Joliot, and Fermi, showed ‘two or more’ free neutrons came out with each fission of U 235. This encouraged speculation about a possible chain reaction. But, again, this was a purely experimental result.