I'm not sure I understand this question. The United States didn't fight a war with "Vietnam", they intervened in a pre-existing war between North Vietnam (and their Viet Cong Allies) on one side and South Vietnam on the other side.

The beginning of American involvement in Vietnam was characterized more by financial and material support, and advisors, and then the US committed significant numbers of combat troops. There was never a situation where the US and "Vietnam" were at peace, and had some sort of a dispute, and then it escalated into a war between the US and "Vietnam".