Stephanus of Byzantium notes the 5th century historian Hippys of Rhegium in his entry on Arcadia (roughly translated):

Hippys of Rhegion (FGrHist 554 F 7) is said to have been the first to describe the Arcadians as people who existed before the moon.

Similarly, Plutarch in Questiones Romanae 76 indicates that the Arcadians are called pre-lunar people. A fragment of Aristotle attests too to this claim (F 591 Rose) that the Arcadians also were proselenoi, ie older than the moon.

Substantial effort was dedicated to claiming the extreme antiquity of the Arcadians. See Daniela Dueck "A lunar people" Philologus 164 (2020) pp 133ff. These claims were repeated by some Romans: Ovid Fast 2.289ff notes that the Arcadians are said to have been in their land from before the birth of Jupiter and are older than the moon.

The most widely accepted theory for the moon's formation is that it was created by a giant impact between the Earth and a Mars-sized object around 4.5 billion years ago. Anatomically modern humans are first attested archaeologically some 195,000 years ago with earlier hominids such as Homo erectus having emerged some 2 million years ago.

Sumerian texts indicate that a moon deity was worshiped from the dawn of writing there around 3500 BC some three thousand years prior to the fifth century BC; worship of this lunar deity, Nanna, continued through to the 3rd century AD well into the common era. Presumably the worship of the deity reflected the existence of a large bright nocturnal celestial object within 500,000 kilometres of the Earth.

Some interpretations read the word proselenoi metaphorically to mean "before time" (because the moon is used in lunar calendars). I believe that the moon was created after the creation of time; this implies that the Arcadians also were created after the creation of time. Either way, I suggest this – whether it be the claim of Arcadians or of Hippys or interpreted to mean "before time" – is bad history.

Edited to normalise spelling and italics.