Does it end slightly earlier?
Whether it was the bombs, the Russians, or a combination of the two, together is something which gets tossed around semi-regularly in threads about the end of WW2 in the post-1900 forum (and occasionally in nuclear weapon related threads in political chat.)
There was a third factor present in August. In July the estimates for the 1945 harvest were made available to the cabinet. The rice harvest estimate in this is usually cited as 'catastrophic'. That item may be hyperbole, but the various analysis or judgements I've seen of the situation are not favorable for the Japanese ability to resist. No matter how one parses it out it looks like the overall caloric allotment in the food rations would fall significantly, from their already inadequate levels.
This harvest report was not close to ready in May, the raw data for the various crops not yet existing or processed. Neither was it clear how much further imports would fall in the next few months. The latter was much clearer after another two months of failure to ship in adequate reserves from the mainland. Neither was the Red Army remotely ready to attack on the desired scale in May. Of course a attack could have been made, but it would have been mostly attritional battles along the borders, with far less ability to advance into the interior of Manchuria or Korea.
What would happen if the atomic bombs were ready to deploy in May?
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This can be read as either just the two bombs actually used, or if the same production schedule of OTL is advanced 90 days. In that latter case we are not just looking at two bombs, but at least one more Plutonium bomb ready for use in less than ten days after the second of OTL was used. So, in less than a month Japan is hit by three such weapons in less than three weeks. & remember the firebombing attacks did not cease, and the smaller air raids on the transportation system, the airbases, the naval bases, the Army logistics depots, the smaller industrial sites, all continued. The USN was participating in these, with the carriers raiding the ports and sinking any remaining cargo and war ships.
Its not as if all other attacks ceased with the use of the two atomic weapons. The air assault was being ramped up in all aspects and was planned and ready to continue escalating as August rolled on into September & October. Set the atomic weapons ahead to May and nothing need change with the rest of it. The fire bomb attacks continue, the smaller more precise Navy and Air Force raids ramp up. The subs continue sinking ships at sea. Food still rots on the docks on the Asian coast.
The escalating attack applies to the atomic weapons as well. Rhoades in 'The Making of the Atomic Bomb' estimates at least five more bomb cores would have been shipped to Tinian by November, or five more bombs in the 90-100 days after the first was dropped. Thats the low estimate. Other estimates vary widely, with the original projections for the design of the Haniford Plutonium production facility being twice that of Rhoades estimate. While problems and delays from the hasty fastback construction, and inexperience abounded, its not ASB territory to speculate six or seven Plutonium bombs could be available in 90 to 120 days from 8 May. Then there is the question of additional Uranium bombs. A decision was made to complete just one Uranium bomb, but the wherewithal to build more was present.
Bottom line here is: Japan would have been subject to the same increase in conventional bombing and other direct attack as OTL over the next 90 days from 8 May to 8 August. AND, at least six atomic weapons could have been used as well. How the cabinet, emperor & the Zaibatsu would have responded to this? Draw your own conclusions.