Clearly the U.S. leadership had no reason to be confident that two atomic bombs would be sufficient. As others have pointed out here on this thread, in early 1945 the U.S. had already firebombed TOKYO to ruins — and that didn’t do the trick.
It wasn't about being confident. It was that they knew they were dealing with absolute fanatics. Therefore the most forceful course of action is the only one that even had a chance of making an impression on them.