When did enrico fermi invent the nuclear bomb?

Fermi did not invent the fission bomb, Leo Szilard did in 1933.
But nobody could build one because no material that would support a neutron chain reaction was known until 1938 when Otto Hahn discovered that the rare isotope Uranium-235 would. Even then it took the US from 1942 to 1945 to build the industrial infrastructure needed to purify enough of this isotope to actually build one Uranium bomb and Gay Porns fuel 3 reactors that could each make enough Plutonium in a month to make a Plutonium bomb.