Maybe I’m falling victim to ex post rationalization, it strikes me that it was pretty much inevitable that the US would use the atomic bomb once it had it.
The thing that saved us from a nuclear war beyond the two bombs dropped in Japan is that it took the US until the early 1950s to get its nuclear weapons production line working smoothly enough to assure sustained high production levels of weapons, and by then the USSR had nuclear weapons as well. The US had originally aimed at being able to produce three weapons a month after August 1945, gearing up to much more in 1946, but the end of the war and problems with uranium and plutonium production meant effectively a two year hiatus in large scale nuclear weapons production, and slow halting production for a few more years, with sustained high level production only after 1950.
So we never got to a situation where the US had both enough atomic bombs to cover its initial target list for the USSR (about 250 targets) with assurance of follow on weapons, and the USSR did not have atomic weapons as well.
So it seems that the real question is how dropping the bombs in Japan affected how management and resources for the US atomic bomb production line were handled. If the US had gotten 1000 weapons assembled by 1950 it might have handled the USSR and China differently. As it was, the US didn’t get up to those numbers of weapons two years later.