If we had invaded Japan, we would have to have killed just about every man, woman, and child in the country. They were preparing to fight using bamboo spears. And our casualties would have been in the hundreds of thousands. Counter-intuitive as it sounds, the bombs saved millions of lives.
One estimate I saw years ago stated that a conventional invasion of Japan would have extended the war through at least 1946 and would have cost 5 - 6 million Japanese lives and one million additional American casualties.
The A-bombs, as you said, saved millions of lives.
In 2005, I spoke to the gentleman who was a ground crew chief for my late dad’s England-based B-17 bomb group base. He told me two interesting things: 1) That Stalin stopped working on the bomb after Hiroshima and Nagasaki, and 2) Hiroshima and Nagasaki saved close to a million Allied lives. I believe him.