While the United States was not involved in any wars during Trump's presidency, he was not the only president in the last 72 years of whom that was true.
Under Article I, Section 8 of the United States Constitution, only Congress is given the power to declare war:
[The Congress shall have Power . . . ] To declare War, grant Letters of Marque and Reprisal, and make Rules concerning Captures on Land and Water; . . .
According to the official website of the U.S. Senate, this is a power Congress has used 11 times, starting against Great Britain in the War of 1812. The last time that power was exercised by Congress was in the midst of World War II, on June 4, 1942, when it declared war against the small Axis countries of Bulgaria, Hungary and Rumania (now Romania). The U.S. was already at war with Japan, Nazi Germany and Italy at that point.
Under this definition — to be a U.S. war, Congress must declare it so — Trump is not the only president in the last 72 years without a war. No presidents in the last 72 years have presided over an official war declared by Congress. This definition is obviously too restrictive. As the Senate website notes, "Since [World War II, Congress] has agreed to resolutions authorizing the use of military force and continues to shape U.S. military policy through appropriations and oversight."
Counting the various conflicts commonly referred to as "wars" by historians, we must include the Korean War, the Vietnam War, the Gulf War, and the Wars in Iraq and Afghanistan as full-scale wars. The Korean War was started under Harry S. Truman, the Vietnam War under Lyndon B. Johnson, the Gulf War under George H. W. Bush, and the Wars in Iraq and Afghanistan under George W. Bush.
By this metric, Trump joins nine other presidents since 1952 — Dwight D. Eisenhower, John F. Kennedy, Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Reagan, Bill Clinton, Barack Obama and Joe Biden — as having "had no wars."
This might still feel slightly disingenuous, however, because several of those presidents helped to escalate those conflicts and therefore the U.S. should be considered to have been involved in them. This means we must also count Eisenhower, the president at the end of the Korean War and the first to place troops in Vietnam, both Kennedy and Nixon's actions in Vietnam, Cambodia and Laos, and Obama's expansion of U.S. operations in Iraq and Afghanistan.
This leaves a shorter list of Ford, Carter, Reagan, Clinton, Trump and Biden as presidents who have not been involved in wars. Unfortunately, we're still not done, because Reagan and Clinton sent U.S. troops to other conflicts. As examples, Reagan ordered the full invasion of the island of Grenada in 1983 and Clinton sent troops to Yugoslavia during the Bosnian War.
This leaves us with Ford, Carter, Trump and Biden as not having been involved in wars.
A true pacifist could point to the Congressional Research Service's list of all uses of U.S. troops abroad, and by that metric, all of these presidents have ordered military actions. Ford used military forces during the 1975 evacuation of Vietnam and 1976 evacuation of Lebanon, Carter used forces in a rescue attempt during the 1979 Iran Hostage Crisis, Trump continued deployments and bombings in Syria (and ordered the drone strike that killed Iranian general Qassem Soleimani), and on Jan. 11, 2024, Biden ordered air strikes against Houthi groups in Yemen.
So yes, Trump has quite a solid record with not being at war. A large part of the withdrawal from Afghanistan and Iraq took place under Trump. However, because Carter and Ford (and Biden, depending on how U.S. involvement in Ukraine, Israel and Yemen develops), are also not considered to have been involved in wars during their presidencies, we rate Trump's statement as False.