IIRC some military dependents were in VN as late as 1966. I was there in 63/64 and there were a substantial number of dependents there at that time. At that time the US effort was known as MAGV, that is Military Assistance Group VN. Later changed to MACV, Military Assistance Command VN. The primary difference was that early on we only had specialists there, advisers, the odd engineer outfit, aviation units from every branch of the services, and lots of intel and civilian folk from almost all the alphabet agencies.
The first draftees arrived in 1965, which most folks regard as the real US ground effort in VN.
We had had advisory personnel there since the late Eisenhower adminsitration, and in 63/64 they had bulked up to 15,000-20,000, depending on who you are listening to. I would vote for the lower number.
I believe that the first acknowledged American KIA was in 1962, although I cannot swear to that year.
Prior to the US build up, VN was considered a good posting for a career military guy(we were almost all guys then), and then got better, and then worse. Some of us were worried the war would be over before we got our ticket punched, of course subsequently many of us got our ticket cancelled.