The Soviet invasion angle is an interesting one. However, I'm not sure whether that's relevant to whether the U.S. should have dropped the bomb or not. Truman doesn't have access to what the Japanese were thinking or not thinking about that. Hell, it's just being speculated now. How would the U.S. be expected to know that.
All the U.S. had to go on was what the Japanese were saying, and how they were fighting. I'm not seeing any evidence that the U.S. was to somehow know they were close to surrendering.
Hundreds of thousands were killed by the conventional firebombings and that didn't cause surrender. Dropping the bombs almost certainly saved Japanese lives.
In fact, I think when it comes to whether it was right or moral to drop the bomb, I think the more damning question is whether it was immoral to firebomb all of Japan for months and months, rather than drop the bomb first. I tend to find the extent of the firebombing more questionable than the atomic bombs to honest.
If two A bombs could have ended the war months and months earlier (and there's no guarantee they would have at an earlier point), was it immoral to wait as long as we did considering the nightly firebombing?