We were already in the process of assembling another Fat Man on Tinian. It wasn't likely to be used like the first two, but we were planning on using about five in Operation Olympic, the invasion of the first Japanese home island of Kyuushuu scheduled to begin three months later. In part because the original plan was blown by Japanese military intelligence for once getting the timing and locations correct, the former from simply logistics, and being believed so that nine divisions of troops had been moved to the island, blowing up the usual math required for an opposed amphibious assault and generally successful campaign. Those who didn't know about the Manhattan Project were planning on using poison gas.
The Soviet program to make nuclear weapons didn't get really serious until we demonstrated they could work in Japan, and their equivalent of our Trinity test took another four years.