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You're correct to assume that there is some context you're missing. Comparing Operation Downfall to the Normandy landings requires a clear understanding of amphibious operations, the scope of each operation, and some rough definition for what actually qualifies as "largest."

Before we go further, I want to be honest about my own limitations here. I’m a hobbyist and not a trained historian. My area of expertise for this community is centered around naval operations during World War II, which includes amphibious operations, but focuses far more on the Pacific than on the European theater. There are several contributors to the subreddit who know more about the Normandy landings than I do. I’m also not an expert on the organization of land-based forces, so if someone comes along and informs me that an Army division was 50 percent larger than a Marine division or something, I’d be grateful for the correction.

A detour before answering your direct question: It's worth pointing out that some people argue that the invasion of Okinawa in early 1945 was actually a "larger" amphibious operation than the invasion of Normandy. Again, it all depends on how you define and measure these things. The landings at Normandy were larger than the landings at Okinawa in some important measurements: More total men landed, more aircraft involved, more total naval vessels. But it's also smaller in several respects. The fleet supporting the Okinawa invasion was much more powerful and more total men were involved in combat operations. We should note here that most people misunderstand what "amphibious operations" consist of. Amphibious operations involve much more than men running onto a beach; it involves the ships that delivered the men to the beach, the ships defending those ships and providing fire support, the aircraft involved, and the supply train to provide materiel for the whole thing. The infantry landing force is just one component.

With that in mind, a key difference between Normandy and Okinawa is the logistical challenge. The invasion of Okinawa and the Ryukus was staged mostly from American bases at Ulithi Atoll in the Caroline Islands and in the Marianas Islands, both of which are well over 1,000 miles from Okinawa. The Normandy landings were staged from Great Britain, only about 100 miles across the English Channel. This meant that airpower could be provided from land-based airfields in Britain; no aircraft carrier participated in the Normandy landings. In the Pacific, the American and British navies brought 16 fleet carriers (an astounding number) and 28 smaller carriers to the invasion of Okinawa. Normandy included six battleships providing fire support for the initial landings and a seventh arriving a few days later (again, land-based airpower helped with the bombardment); the fleet at Okinawa included 20 battleships. The "tail" of the Okinawa invasion also required far more supply vessels that would have been more substantial than the Normandy invasion, if only because the amphibious assault force couldn't wait for supply vessels to sail more than 2,500 miles round-trip to bring more equipment after the initial landings. It's hard to measure apples to apples here, and the Normandy landings may have had more total hulls, but the naval component of Okinawa was larger in most substantive measures. That's borne out further when you account for the total manpower involved, because the more powerful fleet required more men.

Another way to think of this comparison: A service member whose job was to repair and maintain aircraft in Great Britain would have supported the Normandy operations, but never saw combat from his base across the English Channel. Meanwhile, a sailor with a similar job on an aircraft carrier off Okinawa would have come under fire from Japanese air attacks, and his ship would have been shooting back at Japanese aircraft. This distinction means that by some measures, there were more Allied servicemen involved in combat at Okinawa than at Normandy.

The diversion to Okinawa here is worthwhile because the invasion of the Japanese home islands would have looked more similar to Okinawa than Normandy. The Okinawa invasion occurred, in part, to provide a staging location from which men, ships, and land-based aircraft could support the invasion of Kyushu. But Okinawa is still a few hundred miles away from Kyushu, meaning that a larger overall naval component and greater logistics force would have been required to support the invasion.

Now that we've examined how you define "amphibious operation" and "largest" we have to define what constitutes the "Invasion of Japan." Operation Downfall was actually the code name for two separate invasions of Japan meant to be executed in sequence. Operation Olympic was the plan for the invasion of Kyushu, the southernmost of the four main islands of Japan. Olympic was tentatively scheduled for November 1945. Operation Coronet was the name for the subsequent planned invasion of the island of Honshu, the largest of the Japanese home islands. Coronet was tentatively scheduled for March 1946. You can certainly choose to combine these two plans together to measure the "invasion of Japan," but it should be apparent that they're two separate operations divided by several months and hundreds of miles.

The general plan for Operation Olympic was laid out during meetings of the Allies in early 1945 at the Yalta Conference, then refined in May 1945 in the Philippines. Land-based strategic bombers from the Ryukus and the Marianas would help soften up Kyushu in the months leading to the attack. The Navy would impose a more complete blockade of Japan (submarines had already destroyed most Japanese merchant shipping). The pace of operations would then ncrease 10 days before the invasion. B-29s from the Marianas and shorter-range bombers from Okinawa and the Ryukus would target transportation infrastructure that could be used to reinforce Japanese defenses. Naval gunfire would hit coastal defenses. Naval aircraft would do their best to denude airbases of aircraft that could be used in kamikaze attacks.

Large-scale landings were scheduled for November 1, 1945. Nine divisions were scheduled to land in three separate areas on D-Day; three Marine divisions would attack at Kushikino in the southwest (the 3rd, 4th, and 5th), three Army divisions would land at Ariake Bay (1st Cavalry, Americal, and 43rd Divisions), and three more Army divisions (the 25th, 33rd, and 41st) would land at Miyazaki in the east. A tenth division (the Army’s 40th division) would conduct landings on some of the smaller islands just south and west of Kyushu a few days ahead of the larger invasion. Two further divisions (81st and 98th) would carry out a diversion by operating off the island of Shikoku. They'd eventually be committed to Kyushu, making a total of 12 divisions involved when operations began. More than 400,000 men were expected to be put ashore in the first four days of the invasion of Kyushu. Two more divisions (77th and 11th) were slated for follow-on operations. If necessary, further forces that were planned to be used in the invasion of Honshu could be committed to Kyushu in weeks and months afterward.

As mentioned above, my knowledge of Normandy is limited, but it involved about seven divisions (some reinforced) landing on the beaches with three airborne divisions also committed. If you wanted to slant things to present the Kyushu operation as larger, you could argue that airborne operations are inherently different from amphibious operations, and that the seven divisions hitting the beaches at Normandy would have been exceeded by the 10 divisions landing on Kyushu. Of course, that seems to run counter to the spirit of the question; the airborne landings were in support of the amphibious operation and should be counted. That puts you back at 10 divisions for Normandy, give or take some additional units. That means the initial land forces committed to Normandy/Kyushu were generally similar.

The big difference would come down to the overall scope of operations. The Normandy beaches stretched about 50 total miles, while the Kyushu landings would have occurred in three separate areas (four if you include the smaller islands). Kyushu would have included a naval force that was vastly larger than Normandy both in terms of warships and logistics; Chief of Naval Operations Ernest King said the plan called for 3,000 vessels “larger than personnel landing boats,” meaning that those craft are not included in his figure. The air operations also likely would have exceeded that preceding Normandy. The carrier-based aircraft alone might well have exceeded 2,000. Land-based aircraft would include the American 20th Air Force (B-29s in the Marianas), the 8th Air Force (famous for its strategic bombing in Europe), and the 5th, 7th, and 13th Air Forces already in the Pacific. Even if the raw number of bombers was similar, the B-29 was capable of carrying far more munitions than most aircraft participating in Overlord.

This is why it was important to define "larger" and clarify what "amphibious operations" entail. Even if the landing forces were a similar size, the operation as a whole would have been much larger.