At least in film, the first "modern" zombies, the literal dead walking again (as opposed to voodoo and other drug and / or hypnotic states) appear a couple years before Night of the Living Dead. A Hammer film from 1966, Plague of the Zombies, was the first film to show corpses rising out of their graves, digging through the earth, to walk again.
While this is the herald of the modern "truly-dead" zombie, it wasn't until 1968 and George A. Romero that the idea of the "real" modern zombie (actually dead and eating the living) appeared and took root. The fact they weren't called zombies is moot. They were zombies as sure as Nosferatu was a vampire. Also this is only taking into account multiple numbers of zombies. I don't know the earliest film (or other) reference to a singular cursed or other-wise revived person.
And as for Gilgamesh, that is more parable or metaphor. It is not the dead being brought back as rotting corpses (admittedly my understanding of the Epic is sketchy at best). It seems to be the dead being released. I do think there is a difference. Same reason people generally don't think of Lazarus or Jesus to be zombies.