Where do I start? Let’s start with the scholarly consensus.
“The consensus among scholars is that the bomb was not needed to avoid an invasion of Japan and to end the war within a relatively short time. It is clear that alternatives to the bomb existed and that Truman and his advisers knew it”, J. Samuel Walker, “The Decision to Use the Bomb: A Historiographical Update*,” DIPH Diplomatic History 14.1 (1990): 97–114.
Now let’s look at the primary sources material, the actual historical sources.
Admiral Leahy (Chief of Staff to Roosevelt and Truman), wrote this seven weeks before the bombing of Hiroshima.
“It is my opinion at the present time that a surrender of Japan can be arranged with terms that can be accepted by Japan and that will make fully satisfactory provisions for America’s defense against future trans-Pacific aggression.”, Educational Foundation for Nuclear Science Inc, Bulletin of the Atomic Scientists (Educational Foundation for Nuclear Science, Inc., 1985), 36.
After the bombs were dropped he maintained his view that they were totally unnecessary and gave no support to the war effort.
“It is my opinion that the use of this barbarous weapon at Hiroshima and Nagasaki was of no material assistance in our war against Japan. The Japanese were already defeated and ready to surrender because of the effective sea blockade and the successful bombing with conventional weapons.”, Joseph Grieco, G. John Ikenberry, and Michael Mastanduno, Introduction to International Relations: Enduring Questions and Contemporary Perspectives (Palgrave Macmillan, 2014), 210.
When Eisenhower was informed of the decision to drop the bomb, he had grave doubts. He wrote this in his memoirs, recording his reaction when told of the decision by the Secretary of War long before the bomb was deployed.
“During his recitation of the relevant facts, I had been conscious of a feeling of depression and so I voiced to him my grave misgivings, first on the basis of my belief that Japan was already defeated and that dropping the bomb was completely unnecessary, and secondly because I thought that our country should avoid shocking world opinion by the use of a weapon whose employment was, I thought, no longer mandatory as a measure to save American lives.”, Educational Foundation for Nuclear Science Inc, Bulletin of the Atomic Scientists (Educational Foundation for Nuclear Science, Inc., 1985), 36.
In 1945 he expressed his opinion to the Secretary of War that the bomb was not necessary.
“Eisenhower, at least, seems to have expressed the view to Stimson in mid-1945 that the bomb should not be used because, “first, the Japanese were ready to surrender and it wasn’t necessary to hit them with that awful thing.””, Educational Foundation for Nuclear Science Inc, Bulletin of the Atomic Scientists (Educational Foundation for Nuclear Science, Inc., 1975), 40.
In 1945 Hoover sent a memorandum to Truman saying that peace with Japan could be arranged without the need for further conflict (such as the bombs or a land invasion). In 1946 he described this memorandum to Douglas MacArthur. Interestingly, MacArthur agreed with Hoover, saying that both military losses and the use of the bombs could have been completely avoided.
“I told MacArthur of my memorandum of mid-May 1945 to Truman, that peace could be had with Japan by which our major objectives would be accomplished. MacArthur said that was correct and that we would have avoided all of the losses, the Atomic bomb, and the entry of Russia into Manchuria”, Gar Alperovitz, The Decision to Use the Atomic Bomb (Knopf Doubleday Publishing Group, 2010), 351.
MacArthur himself said he saw no military justification for dropping the bomb.
“When Norman Cousins asked MacArthur about the decision to use the atomic bomb, he “was surprised to learn he had not even been consulted. What, I asked, would his advice have been? He replied that he saw no military justification for the dropping of the bomb. The war might have ended weeks earlier, he said, if the United States had agreed, as it later did anyway, to the retention of the institution of the emperor.” (Cousins 1987: 70-71).”, David H. Price, Anthropological Intelligence: The Deployment and Neglect of American Anthropology in the Second World War (Duke University Press, 2008), 305.
Admiral Halsey, commander of the Third Fleet, stated publicly in 1946 that the dropping of the bomb was totally unnecessary from a military perspective.
“The first atomic bomb was an unnecessary experiment. . . . It was a mistake to ever drop it. . . . [the scientists] had this toy and they wanted to try it out, so they dropped it. . . . It killed a lot of Japs, but the Japs had put out a lot of peace feelers through Russia long before.”, Gar Alperovitz, The Decision to Use the Atomic Bomb (Knopf Doubleday Publishing Group, 2010), 364.
Admiral Nimitz said the bomb should not have been dropped, and was completely unnecessary from a military perspective.
“…I felt that that was an unnecessary loss of civilian life… We had them beaten. They hadn’t enough food, they couldn’t do anything.”, Gar Alperovitz, The Decision to Use the Atomic Bomb (Knopf Doubleday Publishing Group, 2010), 364.
Admiral Hill (commander of the Fifth Amphibious Force), said that there was no support among the admiralty for an invasion of the Japanese homeland.
“neither Admiral Nimitz or Spruance (Vice Admiral Raymond A. Spruance, commander of the Fifth Fleet) considered that it would ever be necessary to invade the homeland of Japan.”, Gar Alperovitz, The Decision to Use the Atomic Bomb (Knopf Doubleday Publishing Group, 2010), 364.
Although the president believed that the bomb was necessary to avoid loss of American life in a land battle, Ernest King (commander in chief of the US Fleet and chief of Naval Operations), told him bluntly that it was not.
“The President in giving his approval for these [atomic] attacks appeared to believe that many thousands of American troops would be killed in invading Japan, and in this he was entirely correct; but King felt, as he had pointed out many times, that the dilemma was an unnecessary one, for had we been willing to wait, the effective naval blockade would, in the course of time, have starved the Japanese into submission through lack of oil, rice, medicines, and other essential materials.”, Gar Alperovitz, The Decision to Use the Atomic Bomb (Knopf Doubleday Publishing Group, 2010), 360.
You haven’t read the original sources (see earlier in this post), including the actual tactical assessments of the US military high command.
“Some military commanders argued that neither an invasion of the home islands nor the dropping of atomic bombs was necessary to defeat Japan. If the United States had been willing to wait, said Admiral King, “the effective blockade would, in the course of time, have starved the Japanese into submission through lack of oil, rice, medicines, and other essential materials.””, Dennis Wainstock, The Decision to Drop the Atomic Bomb (Greenwood Publishing Group, 1996), 65.
There was absolutely no need for a land invasion of Japan, and the US knew it.
They weren’t made to save American lives, and the US high command knew that Japan did not have to be invaded. There was literally nothing to do. Commanders of the US air raids were already complaining that they had no meaningful targets left, and that they could not find anything to bomb which was even worth the fuel used to fly out and bomb it. Meanwhile the admiralty was saying a land invasion was unnecessary.