If you see someone beating a child, then as a libertarian, I don’t see an issue with interfering, as this would not be the initiation of force against a peaceful person.
However, you only have the right to use violence to stop the attack. You don’t have the right to inflict harm on innocent passersby in order to stop the attack. You would also not have the right to use force to make anyone else help you against their will. You certainly wouldn’t have the right to carpet bomb the whole neighborhood.
This is where the trouble with having the United States go to war to stop the oppression of a horrible regime. The brunt of the attack will not be borne by the regime, but by the civilian population of the country at question. If you’re trying to help people, bombing them is not the best way to go.
Then you have the issue of what will happen in the attacked country, which will tend to rally around its own flag against the invading US army.
This is to say nothing of the massive theft in either taxation or inflation that will take place to pay for the war.
Then there is the very real possibility that the US government might not be the most humanitarian organization in practice. It was exactly humanitarian purposes that the US claimed in the Spanish-American War. When the Spanish were driven out of the Philippines, the following US occupation was just as bad as the Spanish one was. 200,000+ innocent Filipinos were killed.
So government war would be out on libertarian grounds, unless it was funded entirely through donations. Even then it’s shaky.
Probably the best option would be something along the lines of letters of marque and reprisal. Privately-funded troops going in just after the leaders of the offending government.
I think your question relies on war being extremely neat and precise. It is not.