What nation was the first to beat the US military?

Answer 1

In what context? The British have their battles they'd won against the Colonial Army, the Germans had their victorious battles in two World Wars, as have the North Koreans, Chinese, etc, although they'd either lost the war, or else only managed to bring it to a stalemate.

The war in Vietnam was lost, but, military, the SEATO forces (aside from the US, there were also forces from Australia, New Zealand, the Philippines, Laos, etc.) were very successful against the NVA and VC, and the loss in Vietnam was more a political one. In the war of 1812, the British successfully defended Canada, but failed in their aim at reconquest of the United States.

So, as far as battles go, you could say the British were the first to score a victory in a military battle against US forces. The Vietnamese succeeded in their aim, not by military victory, but by a political one. You could even say the Taliban have had military victories, in a case where they managed to compromise a four man SEAL team (although they took over 100 casualties in this process, as well). So, pick your context.