Truman DIDN’T do ANYTHING.
FDR had all the pieces in place before he died. Truman didn’t even know the bomb existed before he was sworn in as POTUS. All of the orders bearing a presidential signature were signed by FDR. All Truman did was not get in the way.
Truman even tried to manage the bombs’ employment and was ignored. He wrote in his personal diary on 25 July (while he was at Potsdam):
“…I have told the Sec. of War Mr. Stimson to use it so that military objectives and soldiers and sailors are the target and not women and children. Even if the Japs are savages, ruthless, merciless and fanatic, we as the leader of the world for the common welfare cannot drop this terrible bomb on the old Capitol or the new. He & I are in accord. The target will be a purely military one and we will issue a warning statement asking the Japs to surrender and save lives…”
Nonetheless, neither target was purely or even mostly military but Truman made public statements after the first bombing showing that he persisted in believing differently, so apparently he was lied to about the nature of Hiroshima and Nagasaki.
Truman didn’t order the bombings, and the only decisions he took went to nothing because they were ignored.
And OH BY THE WAY, the Japanese surrender wasn’t unconditional either. The Allies scrapped the original Potsdam declaration when they learned through back channels that the Japanese would never agree to anything that threatened the liberty or the traditional role of their emperor, to include charging him with war crimes. The declaration was rewritten putting the Emperor’s fate entirely in MacArthur’s hands. So the surrender instrument they signed bore the word “unconditional” but it was a negotiated uncontidionality (=BS).
Keeping Hirohito in place was the right decision.
We should have allowed the Kaiser to stay in charge of Germany after WWI, at least as a figurehead, would have saved the world a lot of grief.