This is certainly wrong because the first bomb wasn't enough for them to surrender. In fact, the general didn't want to surrender at all and commited suicide after the emperor forced them to stop. It isn't clear under what other conditions Japan would surrender. In my view Japan would probably still control Manchukuo today if not for the bomb.

We can debate after the fact whether using a nuclear bomb was correct but the brutal Japanese regime had to be stopped immediately. We don't have the privilege of knowing the future when making difficult decisions.