Special Activities Division was created in 1947.
Honestly? It would probably be the Special Activities Division of the CIA, rather than any actual military unit.
You can join the CIA without military experience but the Special Activities Division is a highly trained division, most of the SAD agents are recruited from Army Delta or Navy SEALs, so it's very unlikely, I am not saying that is impossible just because there isn't much information about the recruiting process, but I can't imagine a inexperienced person fighting alongside these high skilled soldiers, if there is any position for non military is probably in supporting position like intelligence analyst.
Joy Division was created in 1976.
Brandenburg Division was created in 1960.
Chrome Division was created in 2004.
Queen's Division was created in 1968.
Beauman Division was created in 1940.
Siliwangi Division was created in 1948.
Pansy Division was created in 1991.
The Yellow Division was created in 1954.
Scottish Division was created in 1968.
Division of Banks was created in 1949.