The American plans for invasion definitely existed and were in motion; they were created without any conception of the atomic bombs having a major effect (in fact, the end of the war came fast enough that it produced significant logistical difficulties on the US side).

The invasion plans were called Operation Downfall. They began with an invasion of the southernmost large Japanese island, Kyushu, starting November 1945 (Operation Olympic). This plan was approved by Truman in the summer of 1945. Once Kyushu was secured and could be used as a base of operations, Operation Coronet, the invasion of the main Japanese island of Honshu, would begin. This was scheduled for the spring of 1946. Truman did not approve this in 1945; he was taking a "wait and see" approach to see how things went after Olympic.

You can Google these terms and get lots of information. I think it is important to note that a lot of the literature produced on Downfall is retrospective, e.g., an obsession with "how many people would have died" if it went forward, typically with an explicit aim of justifying the use of the atomic bombs. It is interesting to read the actual discussion that Truman and his Generals had in June 1945, because it makes it much more clear that the estimates of casualties were not very firm at the time and not nearly as high as many later assertions. This is not to say that the casualties would not have been high — it is only to say that there is not a lot of evidence that fears of high casualties played a big role in the "decision to use the bomb."