Well, no, we do know for sure. Paul in Saudi already explained it; it was the combined pressure of the atomic bombings AND the Soviet invasion AND the war generally going terribly, which allowed the civilian half of the Japanese government to prevail.
I’m describing this from memory, so forgive me if I’m oversimplifying, but the manner in which the Japanese government functioned was structurally flawed; the civilian cabinet was supposed to run the country, bu in practice the military reported directly to the Emperor and so could perpetually circumvent the civilian cabinet. The result, as tomndebb points out, was a divided government, but it wasn’t just divided by opinion; it was actually systematically divided in the way it worked. It became possible for the military heirarchy to hide the truth from their own civilian government, to an often ludicrous extent; the catastrophe at Midway was not revealed to any civilian cabinet minister, for instance. The military by 1944 was dominated by officers so obsessed with the death cult of “Yamato damashii” that they were willing to go to stupid extents to keep the war going.
So when CanTak3 claims the Japanese wanted to surrender, and Sam Stone says they would have fought to the death, you have to understand that they are literally talking about two different groups of people; part of the Japanese government which wasn’t insane knew damned well by 1944 that the war was hopelessly lost and wanted peace as soon as it could be arranged, and part wanted to fight to the death. Japan was structurally, organizationally incapable of making the decision to end the war prior to 1945, at least on any terms the Allies could conceivably have accepted.
However, by summer of 1945, the ability of Japan’s military junta to control the country was becoing tenuous, in large part because the country was being destroyed. Even before the A-bombs, entire cities were being annihilated; millions of civilians were simply fleeing into the mountains, and the government’s control of the country was slipping away inasmuch as there was less and less to control. On August 1, five days before Hiroshima, fire bombing destroyed three entire cities. Big ones, mind you.
The August 9 annihilation of Nagasaki, which was the day AFTER Fukayama had been incinerated by conventional bombs, coincided with the Soviet invasion of Manchuria. Prime Minister Suzuki informed the combined cabinet that the war could not continue, and the following week Hirohito broadcasted the defeat speech.
It’s clear from the fact that Japan simply broke under too much straw; specifically, the astounding level of destruction on the week of August 5, combined with the Soviet attack. Had they happened separately, it’s quite likely surrender would not have come at that time; happening at the same time, the civilian arm of government was finally in a position to prevail over the Emperor to overrule the military and accept reality.
As it turns out, of course, quite a lot of military officers were thrilled the war was ending. Hell, a lot of Japanese officers opposed the war in the first place. But the hold of the hardliners over Japanese life was brutal and terrifying; not until the camel’s back broke would anyone dare to oppose them.