Missing the innocent who died in that explosion

Wouldn’t that be “those” explosions?

And, no… they brought that destruction and death upon themselves. They were given warnings, they were given the chance to surrender, but they refused and rejected all entreaties.

F.A.F.O.

vs all the innocent who would have died in a full-scale invasion of Japan...

Indeed. The atomic weapons deployed killed far fewer people than a ground assault would have. They also killed far fewer than the dropping of other ordinance that caused their cities, mostly built from flammable materials, to be reduced to ash and rubble. Japan's people worshipped their emperor as a god and refused to surrender for any reason. Seems under their version of rules of engagement, surrender meant they believed that if they lost, their 'god' would be killed, and they would die as a people group to prevent that. The Allies told them repeatedly that their emperor would not be killed, but they would not listen. Records show, as well, that Japan, like Germany and the US, were each trying to build atomic weapons. Germany was defeated about 3 months before they could complete their program. Coupled with their V2 program? They would've rained atomic bombs as far as they could reach until the whole world capitulated.
War is horrible! Even after the first one dropped, Japan wouldn't surrender. The second one finally forced their hand, allowing the rest of their people to be saved. Bad? Yes. Not as bad as it could've been.

Truman saved lives by using it.

Absolutely! On every level. The estimates at the time were at least a million Allied lives plus the bulk of the people of Japan.

And let's not forget the millions of Chinese that the Japanese tortured and killed.

Learn history.