The primordial darkness associated with the Greek underworld was called Erebus.
Erebus is both a primordial deity—the personification of darkness—and a term for the gloomy region beneath the earth. In Hesiod's Theogony, written in the late eighth century BC, Erebus emerges from Chaos alongside Nyx, the personified Night. Erebus and Nyx then produce Aether, the bright upper air, and Hemera, the personified Day.
Ancient writers did not always use the name in exactly the same way. Homer can use Erebus for the underworld or the dark passage where the dead gather, while later authors sometimes treat it as a synonym for Hades or Tartarus. That shifting usage explains why Erebus may appear as a god, a place, or an atmosphere of subterranean gloom.
Nyx is Night rather than the specific darkness of the underworld. Tartarus is a deep prison or region of punishment, and Chaos is the primordial gap or generative void from which several early beings arise. Erebus is therefore the best single answer for this question, even though ancient Greek cosmology was not completely uniform.