At first this claim seems reasonable, but after doing the research I have come to find that it was not the U.S. as a whole but rather just NATO attempting the expansion. This then led Putin and Russia to want to start their invasion, to which created the war due to themselves expressing that the expansion of NATO should end. This claim is partially true but overall misleading and and exaggeration.
Based on https://www.cato.org/commentary/us-nato-helped-trigger-ukraine-war-its-not-siding-putin-admit-it They state that the U.S. brought Ukraine into NATO, therefore causing Putin to attempt to jump the gun on Ukraine and start a full country invasion on them. But it does not say anything about the U.S. themselves being the only one wanting to make the expansion for them and that rather it was an agreement from all of NATO, and was not primarily the United States fault.
According to NPR https://www.npr.org/2022/01/29/1076193616/ukraine-russia-nato-explainer they claim that the U.S. and Russia say two different things about the bans, that for one Russia said a ban on the expansion was on the table, but the U.S. claims that it's false. They say that it was somewhere in between what they both say. So in total they are saying that it's an exaggeration to say it was the United States fault for the war and invasion.
From https://afsa.org/did-nato-expansion-really-cause-putins-invasion they make it clear that Putins want to invade and begin war did stem from the the expansion of NATO. But they never pinned it on the U.S. but rather just Nato as whole, once again bringing me to understand that this is misleading and an exaggeration.
