I haven’t seen the film yet so I don’t know if they get into this, but a large number of the scientists involved with the Manhattan Project were working because they were terrified that the Nazis would build a bomb before the Allies. When, for several reasons, that failed to happen, they were relieved that the bomb wouldn’t have to be used. They felt betrayed when it was used against Japan, who were not developing a bomb and who could have been defeated using conventional means.
the argument put forward was that continuing the war (with a possible drawn-out ground invasion of japan) would cost more lives than demonstrating 2 nukes.
Yes. that was the argument put forward. Similar arguments have been put forward for almost every military and major terrorist action ever taken. People can subscribe to the justifications, or not, as they see fit. The real thing to be cautious about is if you accept such justifications but only when your country is the one making them.