Truman had been VP for a few months when FDR died ..and he had been kept completely in the dark about the A-bomb until he was sworn in a President. As far as he was concerned, it was just a "bigger bomb"..he didn't grasp what it could do...no one really did. And HST had served in WW I..he'd seen up close the carnage of trench warfare, so when he reviewed the casualty figures from Iwo, Saipan, and the other island campaigns late in the war, there was absolutely no doubt in his mind that he would use/do anything to save American lives..
It is sometimes said that Stalin knew more about the atomic bomb through his myriad of spies than Truman did. This is no doubt true. FDR was arrogant on this score in my opinion. In his dying days he could have briefed Truman in on everything, but he didn't, wanting to hold on to power a little longer. It really wasn't fair to Truman.