You must be the only person then that slept through Yugoslavia, 9/11, the Iraq war, Afghanistan, Libya and others.
https://en.wikipedia.org/wiki/Coalition_of_the_willing
The really bad part is that they were acting during the 'first installment' against people that weren't part of the attack on the United States to begin with (it was essentially a pretext), and the second time they outright lied about the intelligence regarding the WMDs (of which there already was conflicting data collected by the UN weapons inspectors).
NATO’s own resources are essentially office buildings, computer and communication systems, bureaucrats, and seconded military planners. The US didn’t need them for the Iraq War, although it would have liked to have had them involved, because of what that would have meant politically/diplomatically/symbolically.
Despite claiming a broad “coalition”, only three countries actually contributed fighting assets to the initial US invasion - the UK, Poland, and Australia - only the first two are NATO members, and Poland at the time had only recently joined (only 4 years prior). 3 more NATO members (Netherlands, Italy and Spain) provided non-combatant support. I don’t see in what meaningful sense it could be said to be something NATO did.
More NATO members joined in the occupation forces after the initial invasion. But that was never an official NATO operation because those require unanimous approval, and certain member states (most notably France) were always opposed to that.
NATO eventually did become involved in Iraq - training the new Iraqi government’s military. But no fighting ever happened in NATO’s name.
NATO was very careful to obtain requests from the UN in both cases, resolutions 1244 and 1973.
How is Putin ceasing to throw Russia's unwilling and unwitting armed forces onto Ukraine not easy?