Around 400 BC at the latest and around 750 BC (Homer’s death) at the earliest, 3500 years after Adam and Eve.
However, it’s quite possible the elites never worshiped in a polytheistic sense - the earliest pre-Socratics, like Anaximander (600 BC), student of Thales of Miletus (650 BC). Anaximander taught that all natural phenomena were caused by one eternal pre-existent condition of chaos, the apeiron: full-fledged popular Hindu-like polytheism (educated Hindus are often some sort of mono-pan-theist) is not visible amongst the educated even two hundred years after the earliest possible date of Homer’s composition of the Iliad.
By the time of Plato and Aristotle ca. 300 BC, the earliest philosophers of which we have a relatively complete record of teachings from, “Greek mythology” was accepted as pure myth, even if vestiges of polytheism remained in Aristotle (multiple prime movers), but not truly in Plato (everything made sensible by the unitary Form of the Good).
As Gibbon said, and I have no reason to doubt, although he was writing of the Empire, I would project his statement back to the time of Plato at the latest, and likely to Anaximander or Thales: “The various modes of worship, which prevailed in the Roman world, were all considered by the people, as equally true; by the philosopher, as equally false; and by the magistrate, as equally useful” (variously attributed to Seneca, Cicero, or Lucretius).
Now, in other cultures, “true” polytheism - straight-up paganism that is self-evidently absurd - has a much longer tradition, back to scarcely a millennium after Adam was created, amongst the Sumerians, Babylonians, Akkadians, and other ancient near Eastern peoples. Hindu and Egyptian polytheism didn’t come along until quite a bit later, Egypt probably around 2000 BC at the earliest, and Hinduism as we know it was never purely polytheistic. The early proposed ancestor of Hinduism, the “Vedic religion” (which was supposedly purely polytheistic, from what I understand) dates from around the time of Moses (about 1500 BC) according to the commonly-accepted estimates, although it was never written down, and little evidence of it survives. The dualistic Zoroastrianism dates from the middle of the first millennium BC.
The Black Africans (not the North Africans who were converted to Islam and were previously part of the Empire) are not really polytheists but pantheistic-animists, where everything is a god, demon or is suffused with the divine, but there are no good records of 99% of African religion (nor any other aspect of Black African life); it started probably before Islam, and maybe “from time immemorial”.