AFAIK, their war lay primarily in the Pacific, and beyond supporting the Brits and Russians materially, I’m not really sure why the US would want to involve themselves physically in the European theatre. I do feel fear of Germans beating them to the bomb might have something to do with it, but that’s just conjecture.
lets get the timeline straight and the collusion of the allies clear: the atomic bomb was used august 6th. the soviets invaded august 8th. both events were essentially known to both parties; the US had alluded to a new weapon, the Soviets were obliged to enter within a 3 months deadline after VE. the US had specifically began a supply mission to assist Soviet operations in the theater (Project Hula). atomic weapons as a response to Soviet success is utterly unfounded. the bombs being a substitute for invasion is also unsupported, as far as the US warplanners knew they still might've had to invade, for which additional nukes were planned as beachhead weapons.
neither were the Soviets excluded from the peace. Soviet soldiers were not used to occupy the Home Islands (they liberated/accepted surrender north China/Korea) but participated in the allied occupation administration, securing left wing reforms and legality for the communists. these were reversed in '47, not exactly immediately.
I wasn't aware of their involvement in the Allied occupation of Japan, that's interesting. I'll add it to my list of things to learn about