The history of PTSD is a controversial issue. Since the term was coined (and the disorder formally defined) only after the Vietnam War, there is ongoing debate over whether earlier cases of people exhibiting certain symptoms may fairly be used as evidence of the existence of PTSD. Since we can't go back in time and interview people in order to make a formal diagnosis, we technically cannot say PTSD "existed" before the late 1970s. On the other hand, since the particular disorder we now call PTSD is the result of neurologically attested changes in the brain after exposure to traumatic events, we must assume that it is a universal feature of human life, even if we previously didn't know what to call it.
The earliest accounts of symptoms like nightmares, flashbacks, violent outbursts or hysterical blindness in people who had been through traumatic events date to Classical Greece (though some scholars have claimed to recognise PTSD even in Assyrian medical texts). The most famous case is that of Epizelos, an Athenian who fought the Persians at Marathon in 490 BC. The Persians were a particularly terrifying opponent; no Greek community had ever managed to resist their advance, and for the last half-century they had enjoyed an unbroken winning streak in pitched battles against Greeks. According to Herodotos, the Athenians were admired for even standing their ground against this threat, let alone winning. He tells the story of Epizelos' experience:
An Athenian, Epizelos son of Kouphagoras, was fighting as a brave man in the battle when he was deprived of his sight, though struck or hit nowhere on his body, and from that time on he spent the rest of his life in blindness. I have heard that he tells this story about his misfortune: he saw opposing him a tall hoplite, whose beard overshadowed his shield, but the phantom passed him by and killed the man next to him.
Hdt. 6.117.2-3
Lawrence Tritle has further argued that the exiled Spartan commander Klearchos (died 401 BC) was a textbook case. Xenophon describes him as very harsh, bloodthirsty, prone to impulsive action and outbursts of rage; he is said to have believed that an army should fear its general more than it fears the enemy.
Whether either of these cases are evidence of what we would now call PTSD is a matter of debate. Certainly, they are evidence of extreme changes in a person's physical and mental health as a result of traumatic experiences. However, the Greeks would not have recognised them as two faces of the same disorder, and had no mechanisms in place to support or treat cases like these.