around 1961.
November 16, 1961 John F. Kennedy ordered more help to be sent to the aid of South Vietnam. President Kennedy was concerned over the advances being made by the Vietcong guerrillas.
President Kennedy believed in the "Domino Theory" that required Communism to be contained in every instance. Therefore in his first speech on becoming president, Kennedy made it clear that he would continue the policy of the former President, Dwight Eisenhower, and support the government of Diem in South Vietnam.
Eisenhower believed in sending troops, Kennedy did not.
He Sent them to Help The South Vietnamese Against The North Vietnamese
To try and keep South Vietnam from falling to the Communists, and because the government of South Vietnam was too corrupt and incompetent to defend themselves. The government of South Vietnam was never able to defend themselves, and President Gerald R. Ford finally gave up on them in 1975. They soon fell to communist North Vietnam.
Eisenhower sent troops to South Vietnam so they can fight North Vietnam because North Vietnam wanted to take over South Vietnam and they did.
Kennedy sent in the SF & SEALS; LBJ sent in the conventional forces. Those are two different styles of warfare.
1961
President Kennedy sent additional US Advisers & Special Forces (Green Berets) to Vietnam in 1961 up thru 1962. Regular US combat troops did not arrive (officially) until 1965 under President Johnson. Since JFK had troops covertly already arriving in Vietnam by March or April of 1961, he must have ordered them about on his inauguration day of Jan.20, 1961, since it takes a month or two at best/quickest for that to happen...
Kennedy was asked to send additional troops to Vietnam. He sent additional troops and military advisors over to Vietnam to help.
Somewhat democratic South Vietnam was a member of the South East Asia Treaty Organization (SEATO), so by treaty, we were obligated to help defend South Vietnam. We entered the Vietnam War to help South Vietnam stop Communist North Vietnam from their attempts to unify the whole country.