So here's one common misconception in your statement: it was never a question of invasion versus atomic bombs. It was atomic bombs and, if no surrender followed, invasion. The invasion was still in the works when the bombs were dropped, it was still planned. It didn't get un-planned until after surrender. The people planning the invasion were not privy to information about the atomic bombs. It was never phrased as a decision of "do we sacrifice civilian lives to save soldier lives?" Killing Japanese civilians was already being done as a regular point of business during the war — the bomb was not a new "moral" question in that respect. One of the very contentious points in historiography of the end of the war are the casualty estimates — generally speaking, the casualty estimates reported to Truman and Stimson were much lower than the later ones that usually get thrown around to justify the bombings.

The invasion (Operation Downfall) was scheduled for November 1945. Michael Gordin's Five Days in August talks about this question quite directly, as does Tsuyoshi Hasegawa's Racing the Enemy, and Richard Frank's Downfall. Note that many of these points are very controversial and have been debated for decades and decades — don't rely on just one source.

J. Samuel Walker's "Recent Literature on Truman’s Atomic Bomb Decision: A Search for Middle Ground" article is a great overview of the various debates.