March 1940 to be exact -
https://en.wikipedia.org/wiki/Frisch–Peierls_memorandum
The problem is that as soon as that calculation is made and verified, an atomic bomb WILL be built. By 1940 the British MAUD committee had already put together a costed proposal for building a weapon, leading James Chadwick to comment "
I realized that a nuclear bomb was not only possible, it was inevitable. I had then to start taking sleeping pills. It was the only remedy." By some time in the middle of 1941 in OTL, Churchill had decided to support the project and resources, etc. had been allocated - but about the same time Marcus Oiliphant had been going around the US Uranium Committee, banging his fist on desks and using the word "bomb" a lot: this got the US actively involved, and the Manhattan project followed directly on from it. Nor can you just butterfly Frisch-Peierls away: the Japanese and Soviets had come to the same conclusion, and would eventually have built a working weapon.
If you want to see the effect of a delayed atomic bomb on Japan, that's straightforward -
Downfall is pretty good here, the US had pretty much shifted to a strategy of blockade & bombardment by August 1945. That means the Japanese rail and coastal shipping networks are destroyed from the air pretty comprehensively, and that means mass starvation in Japanese cities, and probably several million dead plus the Emperor's head on a pike. One of the reasons the Japanese surrendered when they did was the real fear of a revolution at home if they didn't do something - and with the US blockade strategy about to bite a hell of a lot harder, a civil war seems highly probable in the circumstances.