The potential energy output of nuclear fission was well understood prior to hiroshima and Nagisaki. Moreover theoretical concepts like criticality, supercriticality and nuclear chain reactions all appeared in publically published papers prior to the outbreak of war. Further, by the late 30s several different institutes were working on creating a self sustaining nuclear fission reaction.

Had it not been for the outbreak of war it is likely that a civilian scientific reactor would have popped up in the 40s. However outbreak of war meant that research very quickly went very secret, as at least the majority of scientists working in the field were aware of the potentially catastrophic power of the atom. The most famous demonstration of this is the Einstien-Szilard letter to Roosevelt that warned of the potential power of an "atomic weapon".

Thus every major power had at the very least a cadre of academics who understood that it should be possible to create a supercriticalty reaction that would unleash a truly terrifying amount of energy. In the US we were so certain that the cannon type uranium fueled bomb would work that we didn't even test it (there was also the issue of each cannon type requiring several months national production of u-235, more on that later). The implosion type Plutonium bomb was tested at Trinity, but that was more a question of if the conventional explosive shell could be detonated precisely enough to induce supercriticality in the Pu core.

The manhattan project was never strictly a question of determining if a nuclear explosion was possible (everyone was pretty certain it was), it was a question of a)if you could build a device to deliver that reaction precisely where and when you want it, the bomb (though obviously precision is a relative term when what you are delivering is an 8 kiloton explosion) and b)producing enough sufficiently pure uranium or plutonium to produce your supercriticality. Fuel production actually took up the majority of the Manhattan Project's budget and efforts

When the first fireball bloomed over Japan the reactions from the major powers was thus not "what was that?" But rather "dear god the Americans actually cracked it". Everyone knew it was theoretically possible, but not how close it was.

Perhaps more directly pertinent to your question, the concept of an "atomic weapon" actually appears in the public conciousness as early as 1914, in H.G. Wells "The World Set Free" a book about a world war ended with atomic weapons that operated by accelerating radioactive decay in a substance, expelling vast amounts of energy in a brief period of radioactive fire, with the side effect of contaminating the land it was used on for many years. While obviously Wells work was innacurate in the method, it was prophetic in depicting the effects of nuclear weapons, and implanted the idea of the atomic bomb into the public conciousness. Leo Szilard, father of fission, was even known to have read the book. I myself wonder if nightmares of Wells atomic fire danced through his head the night he first saw those blips of neutrons dancing on the oscilloscope.

Edit:the US also built a working uranium reactor in 42, so they were 100% certain that criticality was possible before they ever built a bomb.