So see this recent answer I wrote to a similar question, which goes into the "timeline" issue. They essentially did surrender after the bombing of Hiroshima, but by "after the bombing of Hiroshima" one should change it to "after they investigated the bombing and made sure it was legitimately what Truman said it was — which took a few days — and also during that time the Soviets invaded Manchuria." Even then they didn't unconditionally surrender until their first conditional surrender was rejected by the US and there was an attempted coup.

Anyway, nobody serious says that the Japanese were "about to surrender" prior to Hiroshima. What they say is: Japan was on the brink of defeat (which is not the same thing as surrender), had people in the high command who knew this fact, and some of those people were seeking ways to end the war diplomatically (e.g. through a negotiation), but were not clear how exactly to do this, and were stymied by the US insistence on "unconditional surrender" which they interpreted as possibly meaning the end of their Emperor system, which they saw as unacceptable. So that's a more complex situation. And indeed, even after the atomic bombs and invasion by the USSR, they were still hung up on that "condition" for several days.

Perhaps it would be helpful to know, what is often referred to as Japan’s surrender of August 15 would technically, and more accurately, be described as a cease fire.

It was not up to the Emperor to declare a surrender. It was two days after the destruction of Hiroshima before Japan’s “big six” military leaders met to discuss the matter, and they decided to fight on. Be mindful that greater destruction previously befell Japan through conventional weapons, so the loss of life and property due to the nuclear weapon was not entirely unprecedented (even if the psychological effect was different). Russia then entered the war with Japan, and the Americans dropped another bomb on Nagasaki.

The big six leaders again gathered to discuss the situation. They discussed America’s call for surrender. They discussed suing for peace in hopes of gaining more favorable terms. They discussed retreating to a remote where they might regroup and continue the fight. On the matter of surrender, they were deadlocked three to three. So the war continued.

On August 12, Japanese Admiral Mitsumasa met with the emperor and suggested that the atomic bombs and Russia’s entry into the war were “divine gifts” which provided an excuse to end the war. With this urging, the emperor summoned the big six to convene once more. They voted on surrender once again, and still were deadlocked.

So the emperor implored them to surrender. While not unanimous, the next vote was finally in favor of surrender. But this still didn’t guarantee a surrender, as a military coup was attempted. The coup failed and a recording of the emperor’s proclamation that the Japanese people must endure the unendurable (he made two copies, in case one was intercepted before it reached the broadcast facility) was finally made public on August 15. His statement never used the word “surrender.”

Still, that wasn’t enough to end the war, as Japan continued fighting with Russia and China and elsewhere, and allied POWs continued to be held gun point. The emperor sent another “surrender” message to his military on August 17. Even then, POWs were still held by the Japanese military and these starving and desperately ill prisoners (including civilian men, women and children) were still being denied food and medicine. For them, liberation came much later ... too late for many.

The official surrender took place September 2. Many Japanese soldiers ignored the decree and continued to fight for months and years and decades (you can easily find accounts occurring on various Pacific islands for an incredible period of time after the rest of the world accepted the war was over, as it was so difficult to fathom that surrender was possible).

The cultural pressures to fight on were great. The civilian population — including women and children — was being prepared to fight allies with sharpened sticks. Literally tons of acorns were being stockpiled as food. The Japanese people were preparing to defend their nation to the bitter end. “Enduring the unendurable” was more about the indignity of surrender than the prospects of death.

Your question goes directly to the issue. The Japanese were not “about to surrender.” They were digging in for an honorable fight and defeat and death.

If you want a serious review of the facts, a great deal of quality research has been done on this topic. One example is “Downfall” by Richard B. Frank.