The Japanese were seeking assistance from the (then-neutral) USSR to negotiate a conditional surrender during the summer of 1945. The US knew this (because they had cracked Japanese diplomatic ciphers) and the USSR deliberately stalled (because they wanted to get into the war). There were members of the Japanese high command (including the Emperor) who supported this diplomatic resolution of the war, but there were also many others, particularly the leaders of the military, who were as of that point strongly committed to the idea that the United States would be reduced to more favorable terms by their presumed planned invasion.

Could a surrender have been negotiated prior to August 1945? I don't know, nobody knows. It wasn't pursued. It would have been tricky. If the US had modified its surrender requirements so as to meet the chief Japanese objection — the unresolved question of the Emperor's postwar fate — would it have helped? Maybe, maybe not.

The first atomic bomb was dropped on the morning August 6. The USSR entered the war and began the invasion of Manchuria at midnight August 8/9. The second atomic bomb was dropped on the morning of August 9. A condition surrender was suggested by the Japanese on August 10, but rejected by the United States. After an attempted coup, the Emperor broadcast an acceptance of unconditional surrender on August 14.

That's the basic timeline. What influenced what? What was necessary? These are not easy questions to answer, because history is not a math equation where you can factor out one complex variable from others. There are some (including military officers from the time) who have suggested that if you remove the atomic bombs from the equation, the Japanese probably would have surrendered prior to the planned invasion (November 1) anyway. The Soviet entry into the war did have a large effect on the positions of the Japanese high command. But disentangling that from the role of Hiroshima is not easy to do. The bombing of Nagasaki does not seem to have changed their views at all in any marked way; there are many who have argued that it was entirely unnecessary. Even then, after two atomic bombs and the Soviet invasion, it still took another 5 days for the Japanese to accept unconditional surrender.

Sometimes when this sort of thing gets brought up, the idea that the atomic bombs weren't necessary is seen as a modern "revisionist" view. A useful counterpoint to that accusation is the conclusion of the US Strategic Bombing Survey from July 1946:

Based on a detailed investigation of all the facts, and supported by the testimony of the surviving Japanese leaders involved, it is the Survey's opinion that certainly prior to 31 December 1945, and in all probability prior to 1 November 1945, Japan would have surrendered even if the atomic bombs had not been dropped, even if Russia had not entered the war, and even if no invasion had been planned or contemplated.

One doesn't have to agree with their conclusions — they had their own reasons for arguing this and certainly lacked the hindsight given by historical research — but it does serve to show that this question was a live one even at the time.

For further reading: a source that goes very carefully over the US, Soviet, and Japanese perspectives in the final weeks of the war is Hasegawa's Racing the Enemy, which is useful even if one doesn't totally buy his conclusion that it was the Soviet invasion, and not the atomic bombs, that ended the war. You might also find useful two articles that I have written: Were there alternatives to the atomic bombings? (answer: yes, for better or worse), and The decision to use the bomb: A consensus view? (which goes over how historians have tended to view these things in recent scholarship).