There were multiple options for the US and its allies near the end of the war, and one of the problems with the way we remember the atomic bombings is that they often are framed as an either/or -- that is, we destroy Japanese cities with atomic bombs or we have to invade the home islands -- when the situation at the time was very much of a both/and scenario.

American B-29s were already striking from islands near Japan, firebombing cities with the specific goal of destroying them and causing large numbers of civilian casualties; American submarines were sinking Japanese merchant shipping, and American and British aircraft carriers were carrying out raids on the Japanese home islands by the time the atomic bombs were used. The USSR also launched an invasion of Japanese-held territory in Manchuria at about the same time as the atomic bombings -- it's still not clear whether that invasion or the bombs themselves were what tipped the Japanese into surrendering. You can find out more about that in this section of our FAQ: https://www.reddit.com/r/AskHistorians/wiki/faq/militaryhistory/wwii/usa#wiki_the_atomic_bombs.2C_aka_questions_.2Fu.2Frestricteddata_has_answered

Regarding the specific claim you're asking about, it's most likely the often-repeated idea that an invasion of the Japanese home islands would result in fewer casualties than using the bomb. Again, see u/restricteddata's answer to this question -- this is very much a narrative that happened after the war, and was not a concern of war planners at the time.

We often see the decision to use the bombs as one that Truman agonized over, weighing killing Japanese civilians versus lives lost in an invasion, but that's simply not what happened -- he went along with plans to bomb Hiroshima, which he seems to have thought was a "purely military" target, and made an affirmative decision to stop use of more bombs without his express consent only after Nagasaki was bombed.

A better way to ask this question is, "were there alternative to dropping two atomic bombs on two cities within three days of each other?" And the answer is certainly yes — I mean, the initial plan, at the very minimum, was to drop them with a week between them, which is a more reasonable amount of time if one cares about the Japanese verifying that it was indeed an atomic bomb and then deciding what do about it (none of which could have been done prior to the Nagasaki mission).

But even beyond this, there were several alternatives "in the air" at the time, and certainly imaginable. These include waiting for the Soviets to declare war on Japan and seeing if that, by itself, was enough. Or doing a "demonstration" of the bomb prior to its use on a city (or just using it on a "purely" military target, to avoid civilian casualties). Or modifying the surrender demands along the lines they knew the Japanese were hoping for. And so on.

Would these have worked better, in the sense of ending the war sooner with less loss of life? Obviously it's hard to know — we can't "re-run" history as if it were a simulation. Could some of these have been at least partially pursued if the goal was to decrease the human cost of the end of the war, and give the Japanese some actual options? Probably.

But you have to remember: the goal wasn't to decrease the human cost of the end of the war. The goal (at least one of them) was to end the war. At no point did the people involved in the planning of the atomic bombs attempt to minimize civilian casualties; in fact, almost every decision they made was about maximizing destruction to urban areas. One can read their target meeting deliberations if you want to get a sense of their mindset. One can understand why this was, in the context of the war and the bomb, but it is important not to fall into the rhetorical trap of thinking that they were trying to minimize casualties. They weren't.

Yes, the most famous of these plans was Operation Downfall, which was a two part operation (Olympic and Coronet) slated for November 1945. Planning for this type of invasion was first discussed in 1943, long before the Trinity test in July 1945, but, once they were available, the bombs were thought of as a superior first step than an outright invasion. As the other responder noted, the dichotomy between bombs or invasion was largely a postwar phenomenon. Most thought the Japanese would not surrender even after the bombs were dropped and that an Allied invasion would still be necessary.

There was debate within some American intelligence offices, particularly the Office of War Information, whether forcing Japanese surrender (whether by bomb or invasion) was really necessary at all. Some OWI projections, including those made by Ruth Benedict's team, claimed that Japan would be forced to surrender in late 1945 or early 1946 due to food and materiel scarcity. Ultimately, these sources of opposition were disregarded by the military. These debates can be found in the Office of War Information papers at NARA II in College Park, Maryland as well as in Alexander H. Leighton's Human Relations in a Changing World (1949).