It would make sense if they did have a experimentation of an A-bomb after rumor got around that the westerns had a powerful bomb in the years of about 1942 more or less.

Japanese physicists knew long before 1942 that an atomic bomb was feasible. Tadayoshi Hikosaka wrote a book about atomic physics in 1934. Physicists all over the world were coming to the same conclusions around the same time and that is why so many countries were working on nuclear programs at the same time. The theory was well known it was procuring and purifying and nuclear material and figuring out how to actually assemble it as well as assembling a method of delivery that were the difficult parts.