After taking Okinawa, the U.S. began building 25 airstrips, each of which could field 25 B-29 bombers, each of which could carry a bomb payload of 20,000 lbs. Meanwhile, Japan had practically nothing left that could fly.
"During 1945, the Japanese military began stockpiling hundreds of Tsurugi, other aircraft, Ohkas, and suicide boats, for use against Allied forces expected to invade Japan. The invasion never happened, and few were ever used."
The date of the Soviet invasion had been agreed between the Allied Powers at Tehran and Yalta. The Soviets were ready on August 5, the day before Hiroshima. So no, the Soviets did not invade because the U.S. used nuclear weapons. A better case could be made the U.S. used nuclear weapons because the Soviets were about to invade.
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