Since there never was a declaration of war and American military advisers were present very early in Vietnam, the commencement date of the Vietnam War is a matter for debate.
Some view December 1956 when Hanoi authorized a low-level insurgency in South Vietnam as the start date, while some consider September 26, 1959 when the first battle between the North communist and South Vietnamese forces occurred. Some argue it should be on June 8, 1956 when U.S. Air Force Technical Sergeant Richard B. Fitzgibbon Jr. became the first American to die in the conflict. Others insist that the conflict only started after the first U.S. bombing operation in Vietnam called Operation Pierce Arrow on August 5, 1964 in retaliation for strikes against U.S. destroyers during the Gulf of Tonkin incident.
On November 06, 1998, after an extensive review of qualifying criteria, the Department of Defense officially lists American deaths in Vietnam from November 1, 1955 – which, in other words, could be now considered as the start date of the Vietnam War or Vietnam conflict, to be precise. That was the day when the Military Assistance Advisory Group (MAAG) Vietnam was created from the MAAG Indochina, which had been established since 1950 under President Harry Truman, to support South Vietnam in their war against the North Vietnamese communists.
Refer to when was the Vietnam war? as well.