The first thing you need to consider is what did Truman and the Joint Chiefs of Staff know in mid 1945 and what did they foresee going forward against Japan. Roosevelt went to Yalta with two goals in mind. He wanted a Soviet commitment to join the United Nations and he wanted the Soviet Union to join the Pacific War. To induce Stalin to join the Pacific War Roosevelt promised the return to the USSR of the territories taken by Japan in the Russian Japanese War of 1905. Stalin agreed to both committing to attack Japanese held Manchuria 90 days after the German surrender. At that date there was uncertainty about the atomic bomb. Admiral Leahy, Roosevelt's Chief of Staff is reported to have said "This is the biggest fool thing we have ever done. The bomb will never go off, and I speak as an expert in explosives." After that the US had suffered 25,851 casualties at Iwo Jima and 48,000 at Okinawa. The next operation, Olympic, the invasion of Kyūshū, was scheduled for November 1; with Coronet, the invasion of Honshu , on March 1, 1946. Casualty estimates ranged from 500,000 to 1,400,000. There also was concern because had reinforced Kyūshū; leading at least some US planers and Admiral Ernie King to question if the planned invasion force was large enough. On July 26, 1945 the US, Britain and China issued the Proclamation Defining the Terms of the Japanese Surrender, the Potsdam Declaration. It called for "We call upon the government of Japan to proclaim now the unconditional surrender of all Japanese armed forces, and to provide proper and adequate assurances of their good faith in such action. The alternative for Japan is prompt and utter destruction." This was broadcast to Japan but never delivered via neutral diplomatic channels. The Japanese cabinet was divided with the Army and Navy Minsters in favor of fighting on the civilians at least leaning in the direction of surrender. The Japanese Prime Minister responded in both Japanese and English "My thinking is that the joint declaration is virtually the same as the earlier declaration. The government of Japan does not consider it having any crucial value. We simply mokusatsu suru. The only alternative for us is to be determined to continue our fight to the end" The phrase mokusatsu suru was translated by the allies as "Killing by silence" Several years latter a dispute arose about the meaning of mokusatsu suru with some claiming it meant "to reserve comment" Most historians reject this interpretation. We do know that after the bombs were dropped and the Red Army invaded Manchuria there was another Japanese cabinet meeting where the deadlock between the military and civilian ministers was broken by the Emperor.
Truman, of course, had no idea what mokusatsu suru meant and did not know the phrase had been used. He relied upon the translation given him by the State and War Departments. He generally knew the casualty estimates. He is quoted as saying "We had a bigger bomb so we used it." Although unknown to the Allies at the time post war investigation showed that the Imperial Japanese Army was more upset by the Soviet Invasion that by the atomic bombs. Whether that means anything is doubtful in my opinion. The Red Army went through the IJA like a hot knife through butter and the smug Japanese Generals were undoubtedly embarrassed by their poor showing.
I do not see how the phrase "to reserve comment" indicates an acceptance of the Potsdam Declaration.
There were also some discussions in Switzerland where the Office of Strategic Services representatives was approached by a couple of Japanese businessmen who claimed to speak for the Japanese Ambassador seeking to set up a surrender. The CIA website (
https://www.cia.gov/library/center-...ence/kent-csi/vol9no3/html/v09i3a06p_0001.htm ) has a summary of these discussions including the memos prepared for Truman. These discussions never really went anywhere and I do not think there is a paper record from teh Japanese Embassy back to Tokyo. At most what Truman had was a somewhat prominent businessman representing what the Japanese government was willing to do.
Still another argument is that the blockade of Japan would have forced a surrender within months if not weeks. Presumably the conventional bombing campaign both land and naval based would have continued. IF this would have caused a change in policy and how long it would take are conjectural at best.
To me the key fact is that it took an Imperial decision to overrule the Army and Navy ministers. The military, particularly the Army, had ruled Japan since 1940. Until that happened the official policy was to continue the war.