It wasn't about "surrender talks" and all that — the US were demanding an unconditional surrender, which means no negotiations, and that could be conveyed in a sentence or two. The Japanese were perfectly capable of putting that out (and they didn't need to translate it; both they and the US had plenty of English–Japanese translators). Yes, you later have to sign formal documents. But if the Japanese had wanted to they could have acceded to Allied demands quite quickly. (This is what they did on August 15th, 1945, even though the formal surrender wasn't until September 2nd.)

But the timing was too tight for any reasonable expectation of surrender. Here's why.

The bomb was dropped on the morning of August 6th. The attack was devastating to Hiroshima and its communication lines, though help was sent in quickly from nearby cities. The high command was aware that Hiroshima had been attacked — but they did not know it was an atomic bomb. Everyone assumed it was just another large conventional attack of some sort. Such attacks were happening routinely by the summer of 1945 and people had been expecting that one would come to Hiroshima at some point (its neighbor, Kure, had suffered a firebombing raid in early July that had destroyed 40% of the city, and citizens of Hiroshima had participated in the relief effort).

The announcement from the White House that it was an atomic bomb was not released for 16 hours (as the announcement itself says). There is, by the way, no real understanding of why the delay was so long — General Groves later claimed in his memoirs that he couldn't figure it out, anyway, because it wasn't what was intended.

So that's around 10pm Japanese time. The next morning (August 7th), the Japanese high command meet about this and agree that before they factor this into their thinking, they need to send a team to confirm this claim by the Americans, because it's a big claim and World War II is full of exaggerated state propaganda about new weapons. Even the most die-hard defender of the atomic bombings would agree that if you are going to decide to surrender on the basis of a new weapon you should confirm the weapon is real before you do so.

So they get a team of scientists together from Kyoto and Tokyo (the same scientists who had been working on Japan's tiny nuclear program), and send them to Hiroshima. It takes them some time to get there due to wartime disruptions, and then they have to make various observations about the damage at Hiroshima, take measurements and samples, observe radioactivity levels, etc.

It takes until the evening of August 8th for them to communicate a report back to Tokyo: "What I've seen so far is unspeakable. Tens of thousands dead. Bodies piled up everywhere. Sick, wounded, naked people wandering around in a daze .... Almost no buildings left standing. I'm very sorry to tell you this ... the so-called new-type bomb is actually an atomic bomb."

The Japanese Supreme War Council agree to meet on this the next morning (August 9th). By this point the second bombing mission has already begun. And overnight the Soviet Union will declare war and invade Manchuria, complicating matters even more.

So yeah, it isn't really a reasonable amount of time. Even one day more would not have been a reasonable amount of time for real deliberation about the fate of the nation. (It is not clear, as an aside, that the bombing of Nagasaki had much impact on the deliberations of August 9th. So most historians think it was probably unnecessary in a strict sense — you would have gotten the same result without it. On August 10th, the Japanese offered a conditional surrender to the US, which was rejected. On August 15th, after several other events, they finally agreed to an unconditional surrender.)

But here's the thing. It wasn't meant to be a reasonable amount of time. The US never planned it as, "we'll drop one bomb, and if they don't surrender, we'll drop another." There was meant to be a week between the two bombings, but that was just a matter of expected schedule. The schedule got changed for very non-strategic reasons: the weather conditions. The people on Tinian had no belief that one bomb or two bombs was going to end the war; the people who made the bombs (notably General Groves) thought it might take 5 bombs or so before the Japanese surrendered. Truman had zero input onto whether a second bomb would be dropped, and as far as I can tell, was not even told that it would be. The strike order had a lot of detail about the use of the first bomb, and then essentially said, "you can drop as many as you have available after that at your discretion."

Which is just to say that the idea that they dropped one bomb, then waited to see what happened, then ruefully said, "I guess we have to drop another one"... this is totally false. They were dropping as many bombs as they could according to the time it took them to assemble them and according to the forecast weather visibility on Japan. It was not very "strategic" on any level (except one: the first bombing was supposed to take place after August 3rd, because it needed to happen once the US was no longer at the Potsdam Conference with the Soviets, and Truman was hoping that maybe the Soviet plans for declaring war would be thrown off if the Japanese did, by chance, surrender earlier than expected). Only afterwards, when Japan surrendered, did that entire narrative get rewritten as being a strategic gambit in which it was clear that one or two bombs might end the war. But that wasn't how they thought of it at the time.