Saying it was just an engineering problem is really understating the level of theory and experiment had to happen at the same time. It was a huge scientific and engineering endeavor that happened simultaneously. Some good books that go into the crazy intricacies are American Prometheus and The Making of the Atomic Bomb if you are interested.

I'm reasonably sure that fission was discovered by Otto Hahn and Lise Meitner sometime in the late 1930s, few years after Fermi accidentally split the atom without realizing it.

Yea the theory was not really much before this (https://en.wikipedia.org/wiki/Nuclear_fission#History).

There really couldn't be much theory on this before 1900's anyway because of our understanding of the atom/nucleus.