The goal of the show's approach to history was to be inspired by it but not limited to it. So you should not take it as a historical record of anything. It does, however, base most of its actual events in real discussions, people, and events, even if they are altered significantly. So there were suggestions by scientists, notably the Franck Committee at the University of Chicago, to instead "demonstrate" the atomic bomb to the Japanese in a non-violent way, at least prior to any possible use (to give them the realistic opportunity to surrender beforehand). The military was not interested in this, though it had enough of an effect on the thinking of someone like Secretary of War Henry Stimson that he assigned it as an explicit question to a panel of top scientists (Oppenheimer, Compton, Lawrence, Fermi) who were advising on policy matters. The Scientific Panel unanimously agreed (though apparently not without some difficult deliberation) that the weapon should be dropped on a city first, without demonstration. Such was the highest level of consideration that this proposal was given.

(You can read more about this here, which includes a link to the Franck Report and to the conclusion of the Scientific Panel. Note: I was the historical consultant for Manhattan for its second season.)