My understanding is it was not the US's intent to invade mainland Japan. After taking strings of Pacific Islands from the Japanese, ending with the Iwo Jima bloodbath, I thought it was decided to drop nukes on Japan till they surrendered, instead of invading them (one, to spare American lives, and two to scare the Soviets).
I'm sure that the Soviet army pushing the Japanese out of resource-rich Manchuria would have played a key role in Japan's eventual surrender had the atomic bomb never been invented, but saying that "The Soviet entry into the war played a much greater role than the atomic bombs in inducing Japan to surrender" is a bit of a stretch.
The Soviets may have cut off Manchuria, but Japan still had resources from Korea. And the Soviet Army was separated from the Japanese mainland by sea as well, where they would have been particularly vulnerable had they tried to cross and invade. Compared to the US razing entire mainland Japanese cities with a single bomb, at will... Sorry, don't buy it.
Also, the production of atomic bombs was constrained to around 3 or so bombs per month by late 1945. Which is significant but would have been only comparable (rather than greatly superior) to the destructive power of the conventional strategic bombing campaign. Even without atomic bombs Japan would have been utterly devastated by the end of 1945 had the war continued (every city destroyed, most of its shipping destroyed, most civilians starving and/or homeless).
There was also talk at the top that has since been declassified about the usage of nuclear weapons tactically. As I recall the plan was to stockpile bombs if the Hiroshima/Nagasaki plan didn't work so that they could be dropped tactically to make way for the ground invasion. Keep in mind that if the casualty rate was only 5% of what it had been taking Okinawa, almost 300,000 US troops would have been killed.
In short, there is no doubt that the United States was going to invade mainland Japan. The Japanese were planning to repel the invasion. If the Japanese didn't surrender, millions of Japanese would have been killed in the invasion.
My apartment mate is Army officer whose job is to plan for literally every eventuality - it's what the military does, or tries to. In the case of WWII, not planning a detailed invasion of Japan would have been unfathomable, even if they fully knew the military and political effects and consequences of the atomic bombs.
Which they didn't. I'm pretty sure a few did - the inventors of the thing for one - but it was still too unprecedented and game-changing at the time to be able to annihilate an entire modern city with a single bomb, and no general was going to risk the war and his career throwing all his eggs into the nuke basket when it was only marginally more difficult to have his staff draw up plans for a full scale invasion as well. Why do one when you can do both? Hence all the standard invasion plans and expectations.
But I'm also pretty sure that Hiroshima and Nagasaki quickly invalidated those plans, because they were based on a prior understanding of the world and of wars that had also become invalidated by the atomic bomb. Had Japan not surrendered after the first two, I'd bet anything that the US would have simply continued to drop nukes on the island until they finally cried Uncle, instead of actually invading, after realizing how easy it was to slaughter hundreds of thousands of Japanese with next to zero risk for US forces.
My point is, the nukes changed the entire calculus of warfare, and did so at the last minute in late 1944 and 1945, and though extensive, documented, official plans had been drawn up to invade Japan, they were invalided by Hiroshima and Nagasaki. There's no way the US would have invaded Japan once they saw how easy it was to simply annihilate the place with a single plane and bomb.
Try this thought experiment: In the history that actually happened, two things occured - the Soviets defeated the Japanese Manchurian Army and at roughly the same time the US nuked Japanese mainland, and shortly afterward Japan unconditionally surrendered. Now imagine two alternate histories:
1) The US fails to invent the atomic bomb, and moves to stage a full scale invasion of the Japanese mainland, while the Soviets still defeat the Japanese Manchurian Army as actually happened.
2) The US invents the atomic bomb and drops it on Hiroshima and Nagasaki as actually happened, but Soviet military failed to organize on their Eastern border, never attacked much less defeated the Japanese military there, and never threatened their hold on Manchuria.
Which of those two do you think would more likely have led to Japan surrendering as it did in our actual history?