Four hypotheses:
1.- Total Blockade and War of Attrition: by 1945 Japan has lost all of its foreign territories and colonies. President Truman and the Allies decide to avoid a costly invasion that would results in the deaths of millions of Japanese nationals and hundreds of thousands of American and Soviet Soldiers. He also wants to avoid the possible division of the country into a Communist Soviet-occupied zone and a Capitalist, American-occupied zone. Japan is unable to trade with any other country. No products or services reach its shores. A naval and Air blockade is in effect and all of its ships and airplanes have been destroyed. All of its industries, ports and airports have been bombed to oblivion and the country is gradually starving and reverting to subsistence agriculture. Without oil, the Japanese deplete all their woods in order to cook and heat their homes. The country becomes victim of an environmental and human disaster. By 1950 it is a desolate land and more and more refugees flee a North Korea styled authoritarian regime. Finally Americans decide to propose negotiations in order to avoid Soviet intervention. Japan accepts to remain neutral and to never send its forces to foreign war theaters without a UN mandate or in the absence of a direct attack but refuses Any American bases. Americans accept but retain Iwo Jima and Okinawa under American occupation.
2.- Unwilling to use the Nuclear bomb against Japan, Americans invite a delegation of Japanese scientists, politicians and military representatives to an isolated atoll. They detonate the bomb and obliterate it. The Japanese delegation is horrified and returns home with pictures and films of the damages and of the explosion. The Japanese offer their surrender but with several conditions and negotiations drag for years. A second bomb is detonated much closer to Japan and the Japanese finally capitulate but their remaining military is intact and they enter into an uneasy alliance with the United States against the Soviet Union.
3.- Impatient to end the war. Americans do not wait until the Nuclear bomb is completed and launch a devastating campaign of bombings throughout the entirety of Japan. All roads, railroads, industries, airports, government buildings and even agricultural fields are completely destroyed. One million Japanese citizens die during the bombing raids and the Americans threaten to destroy the Imperial Palace. International Public Opinion starts turning against Americans and Stalin takes advantage of that to make a proposal to the Japanese to join the Soviet Block. In order to force the Japanese into acceptance he invades the Northernmost Japanese Kuril Islands and annexes them to the Soviet Union. Japan still declines but decides to negotiate with the Americans and has the Soviet Union mediate, deftly playing on the rivalry between the two powers to ensure adaptation of the regime and an armistice. A treaty ensuring the permanent neutrality of Japan in international affairs is signed and the country becomes a sort of Asian version of Switzerland, with a very strong financial sector. Closely allied economically with American and Britain (Hong Kong).
4.- American and Soviet forces invade Japan. 30 million Japanese civilians die in the fighting either as direct belligerents or by committing suicide. 5 million American and Soviet soldiers are killed and even after the utter destruction of Tokio and the Imperial Palace, a guerrilla war continues to be waged against the occupying forces. The Emperor is captured and sentenced to death for war crimes and Japan ceases to exist as an independent nation. American forces occupy the Southern Part, including Tokyo and Soviet forces occupy the northern parts and are seriously considering annexation. In China, the last remaining Japanese forces are eliminated and the survivors are sent to gulags or executed. Tensions run high between American and Soviet occupying forces. In 1955 Americans annex Southern Japan as an oversea territory under direct administration of the armed forces. The Soviet Union follows suite with Northern Japan. A huge demilitarized zone is created by treaty between the two powers.
Americans did invade part of the Japanese home islands such as Iwo Jima and Okinawa. The battles were brutal . 94 % of Japanese forces were killed and Americans suffered enormous casualties. They also decided to starve Japan in order to force its capitulation. Operation Starvation in which a total blockade of Japanese coasts and waterways was imposed, including spreading explosive water mines to prevent any Japanese maritime activities.
They also tried to force Japan into submission with several air raids with incendiary bombs that killed hundreds of thousands of people and destroyed half of all its industry. The Soviet Union did not yet have enough forces to invade Northern Japan but time was in their favor and their Communist Chinese allies would have certainly helped.