For Truman, the bombing of Hiroshima and Nagasaki was justified
The way WWII played out meant that the bombings were the most effective ways of ending the war, preventing further destruction.
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In 1945 United States had, through an Island Hopping campaign, pushed Japan back to its four main Home Islands. President Truman needed either to find a way to force Japan to surrender or authorise an invasion of country.
In the summer of 1945, American military strategists were busy planning the invasion of Japan’s four main islands. The battle of Okinawa, the first assault on Japan’s Home Islands, cost the United States and Japan tens of thousands of soldiers and hundreds of thousands of Japanese civilians. The invasion (Operation Olympic) would be, American military leaders argued, hugely costly not only for American and Japanese troops but also for civilians. The invasion of southern Japan would cost many more lives. Historian Richard Frank argues that given this set of circumstances it is both unsurprising and justified that President Harry Truman gave the order to drop nuclear weapons on Hiroshima and Nagasaki. The United States needed to do everything in its power to avoid the costs both military and civilian that a full scale invasion might result in. Japanese military leaders were gearing up for a bloody invasion. Japan’s four main islands were starved of war material, yet the army was preparing the island of Kyushu to repel American attack.  The Chiefs of the General Staff of both the Imperial Army and Navy believed that, while the war was lost, fighting the United States to a stalemate would assure beneficial terms of surrender. The bombing of Hiroshima and Nagasaki changed this calculation. As the Emperor Hirohito noted in his address to the nation on the date of Japan’s surrender, "the enemy has begun to employ a new and most cruel bomb, the power of which to do damage is indeed incalculable, taking the toll of many innocent lives. Should we continue to fight, it would not only result in an ultimate collapse and obliteration of the Japanese nation, but also it would lead to the total extinction of human civilisation." The bombing of Hiroshima and Nagasaki led Japan’s leaders to realise that continued resistance was futile and surrender before a costly invasion.
Framing surrender as the result of unmatchable American scientific advancements was a much easier and more comforting way to understand defeat than as the result of poor military planning.
[P1] Truman had only two choices to end the war: invasion or bombing. [P2] Human costs of an American invasion would have been huge for both Japan and the United States. [P3] Given the human costs of invasion, bombing was a less deadly way to end conflict.