It is impossible for anyone to diagnose someone with PTSD before such a concept has been described and formally introduced into medical canon. This was done specifically to make sure Vietnam veterans got the care they needed. From the point of view of medical history, then, PTSD was "invented" for the sake of Vietnam veterans, and didn't exist as a concretely understood form of mental illness before that time. So we can never say that anyone prior to the Vietnam War "had PTSD". For a great discussion of the methodological problem, see /u/hillsonghoods' Monday Methods post here.

What we can do is look at whether past societies recorded signs of physical and psychological change in people who had suffered traumatic experiences. There are some famous cases from the historical record that some modern scholars have interpreted as PTSD (though they are never described in enough detail to make such a diagnosis). I discuss some of the Greek evidence here. u/sapere_avde goes into the Roman evidence here. u/kookingpot discusses Assyrian material here.