As @jwenting very correctly said: radios, film and photo cameras, aircraft, and cars existed. Japan also had their own scientists. They weren't exactly stupid.
Their scientists may not have been working on an atom bomb, but they were at least aware such as weapon was possible. They may not have known the exact capabilities of a nuclear weapon, but most certainly knew something like that was on a different level.
So, what was the process, and how long did it take, for Japanese high command in Tokyo to believe that the USA had a super-weapon that could turn cities into melted metal and glass?
Within minutes, most likely. Not much longer than 10-20 minutes. An hour at the most. The highest surviving officer in or near Hiroshima would call his superior who would pass the message upwards. The delay might be due to confusion and finding working telephone lines. 80.000 dead is not everybody dead. I can't find quickly how many people lived that at the time of the bombardment, but I think close to or more than a million. That's <10% casualties. That means lots (>90%) of people survived. Many of them were military officers who would at least attempt to pass on the message.
The reason they didn't surrender immediately wasn't because they didn't believe what had happened, it was because they didn't care.
Partially correct. They most certainly believed what had happened. But they didn't care:
The Japanese high command expected only one or two bombs existed. So Hiroshima was nuked. Big deal. Let them nuke another city if they like that. After that they would have to invade and pay the price in blood.
This is very important:
The whole strategy of the Japanese military command was to make any invasion of Japan so costly in human lives that the Allies would rather negotiate a peace settlement. The Allies had learned that lesson when they invaded Iwo Jima and Okinawa. The Japanese command was convinced the Allies would not be willing to pay that price. They were right. But the Allies an alternative for invasion: the bomb.
My guess is that the atomic bomb was not an "out of the blue" surprise?? Such a super-weapon had been discussed as theoretically possible for 20 years?
There is a very big difference between something that is theoretically possible and the real thing. Theoretically we can fly to Mars and colonize it. In reality we aren't even close to do it. Plans to build a nuclear weapon only got on the way after WW2 had begon. Only one nation, America, had the wherewithal to fight the war and build a nuclear weapon at the same time. Do mind that to deliver the bomb the B 29 had to be developed, and that cost as much if not more than the entire Manhattan project.
The Manhattan Project was no secret.
Entirely wrong, the Manhattan Project was a huge secret. The fact that the USSR was able to penetrate it does not want to say it was open to the public.
@jwenting wrote: It wasn't until the Emperor himself intervened after the second bomb was dropped that the war cabinet bowed to the inevitable.
Even that was not enough. Major Kyūjō tried to commit a coup (more like a hold up of the imperial palace) to get hold of the recording with the speech of the emperor. His goal was to destroy that recording in the hope to continue the war. That coupe came after the high command already had accepted defeat and obeyed the emperors command. The coup was a failure, Kyūjō couldn't find the recording, had to flee the palace and committed suicide.
The most important reason Japan surrendered was not the destruction of 2 towns. All towns were already destroyed. It was the news that Manchuria was invaded and taken over by the USSR. If anything, the atomic bombs were an honorable way out, sort of. ("How could we fight against such horrible weapons?")