One important thing the US could have done to get the Japanese to surrender without dropping the bomb would have been to promise that Japan would not be turned into a republic after the war but allowed to keep its imperial family as ceremonial heads of state. As, you know, actually happened after they surrendered.
Promising to do what we actually did would have been more than enough to save a huge number of lives, and honestly we should have had Hirohito "go into seclusion" in favor of a successor.
But you don't know that promising that wouldn't have emoldened the Japanese leadership. That they wouldn't have seen that as a weakening of Allied resolve and a willingness to end the war on Japan's terms. Japan was already using Iwo Jima and Okinawa to fight to the last man while exacting high American causalities, in an attempt to make the US reassess the cost of taking mainland Japan.
Promising to do what we actually did would have been more than enough to save a huge number of lives, and honestly we should have had Hirohito "go into seclusion" in favor of a successor.