I’ve heard Ike sent the first advisors to Vietnam. Kennedy sent the first troops and Johnson/McNamara used the Gulf of Tonkin incident to escalate the conflict to a full scale war.
The first American ground combat troops were Marine units that arrived early 1965 during the Lyndon Johnson admin.
Kennedy had some 15,000 US advisors in Vietnam, including my father. The number involved in combat would have been very small and largely off the record. Special forces leading their ARVN trainees, things like that.
Eisenhower had 750 - 1,500 American advisors in South Vietnam during his presidency. The Communist insurgency hadn’t grown as large as it would during the Kennedy years.