After watching Alternate History Hub's video on Operation Downfall, I was left wondering what the long-term consequences of nukes being delayed? Let's say that the Manhattan Project suffers enough of a setback that the United States doesn't test its first atomic bomb until late 1946 or 1947. For the post-war let's say that the Soviets managed to take Korea and Hokkaido.
Would the United States publicly announce the existence of the bomb to deter the Soviet Union, or would they keep it a secret until an actual war broke out? If the former, how likely is a war when the world hasn't seen the effects of nuclear weapons yet? If the latter, how soon would a war break out, and how soon would the Soviets develop their own bomb as opposed to OTL?