Theopompus (c.380-315 BC) wrote a history of the reign of Philip II of Macedon, including a digression concerning the fabulous island of Meropis. We don't have the full text of this work, but the Meropis fragment is preserved in the Varia Historia by Aelian, book 3, chapter 18.
On its far border is the land of Anostos ("no-return") which has two rivers, Pleasure and Grief, with fruit trees growing along each. Eating from the Grief trees will cause you to have a miserable life and then die. The Pleasure fruits result in you aging backwards.
The other Trees which grow by the River of Pleasure produce fruit of a contrary nature, for who tasts thereof shall be eased from all his former desires : If he loved any thing, he shall quite forget it ; and in a short time shall become younger, and live over again his former years : he shall cast off old age, and return to the prime of his strength, becoming first a young man, then a child, lastly, an infant, and so die.
(English translation by Thomas Stanley, 1665)
ὃς γὰρ ἂν γεύσηται τούτων, τῶν μὲν ἄλλων τῶν πρότερον ἐπιθυμιῶν παύεται, ἀλλὰ καὶ εἴ του ἤρα καὶ αὐτοῦ λαμβάνει λήθην, καὶ γίνεται κατὰ βραχὺ νεώτερος καὶ τὰς φθανούσας ἡλικίας καὶ τὰς ἤδη διελθούσας ἀναλαμβάνει ὀπίσω. τὸ μὲν γὰρ γῆρας ἀπορρίψας ἐπὶ τὴν ἀκμὴν ὑποστρέφει, εἶτα ἐπὶ τὴν τῶν μειρακίων ἡλικίαν ἀναχωρεῖ, εἶτα παῖς γίνεται, εἶτα βρέφος, καὶ ἐπὶ τούτοις ἐξαναλώθη.
(Greek text from Rudolf Hercher's edition, 1866)
The Meropis account is sometimes thought to be a parody of classical political utopia stories, specifically including Plato's version of the Atlantis legend. Theopompus was a pupil of Isocrates, Plato's rival in Athens. It's possible that the aging-backwards bit is specifically riffing on Plato's Statesman (Πολιτικός), which includes some cosmological ideas about occasional reverses in the flow of time.
In that dialogue, Socrates is joined by a kinsman, "young Socrates", and a Stranger (ξένος, presumed to be the same character as in The Sophist). The Stranger explains that they have heard about two stories, the long-ago "age of Kronos" when people were born spontaneously out of the earth; and that the present east-to-west motion of the sun is attributable to the kingship of Atreus. (From other sources, he'd requested Zeus to change the heavens from their former opposite arrangement in order to prove divine sanction for his claim.)
He says that these are part of a larger history, where God will occasionally stop pushing time forwards, and that it will then flow backwards for a while before God nudges it on again. The moments of reversal are catastrophic. The backwards era is not an exact repetition of the preceding forwards era - natural processes happen in the opposite sense, but people still experience causality as normal. For example, people were "born from the earth" in that the decomposition of corpses happened backwards, causing aged human bodies to spontaneously appear and come to life; on awakening they would begin to grow younger, but would still eat, drink, etc., in the normal way.
A description of what happened when time started to go backwards:
The life of all animals first came to a standstill, and the mortal nature ceased to be or look older, and was then reversed and grew young and delicate; the white locks of the aged darkened again, and the cheeks the bearded man became smooth, and recovered their former bloom; the bodies of youths in their prime grew softer and smaller, continually by day and night returning and becoming assimilated to the nature of a newly-born child in mind as well as body; in the succeeding stage they wasted away and wholly disappeared. And the bodies of those who died by violence at that time quickly passed through the like changes, and in a few days were no more seen.
(English translation by Benjamin Jowett, OUP, 1871)
ἣν ἡλικίαν ἕκαστον εἶχε τῶν ζῴων, αὕτη πρῶτον μὲν ἔστη πάντων, καὶ ἐπαύσατο πᾶν ὅσον ἦν θνητὸν ἐπὶ τὸ γεραίτερον ἰδεῖν πορευόμενον, μεταβάλλον δὲ πάλιν ἐπὶ τοὐναντίον οἷον νεώτερον καὶ ἁπαλώτερον ἐφύετο: καὶ τῶν μὲν πρεσβυτέρων αἱ λευκαὶ τρίχες ἐμελαίνοντο, τῶν δ᾽ αὖ γενειώντων αἱ παρειαὶ λεαινόμεναι πάλιν ἐπὶ τὴν παρελθοῦσαν ὥραν ἕκαστον καθίστασαν, τῶν δὲ ἡβώντων τὰ σώματα λεαινόμενα καὶ σμικρότερα καθ᾽ ἡμέραν καὶ νύκτα ἑκάστην γιγνόμενα πάλιν εἰς τὴν τοῦ νεογενοῦς παιδὸς φύσιν ἀπῄει, κατά τε τὴν ψυχὴν καὶ κατὰ τὸ σῶμα ἀφομοιούμενα: τὸ δ᾽ ἐντεῦθεν ἤδη μαραινόμενα κομιδῇ τὸ πάμπαν ἐξηφανίζετο. τῶν δ᾽ αὖ βιαίως τελευτώντων ἐν τῷ τότε χρόνῳ τὸ τοῦ νεκροῦ σῶμα τὰ αὐτὰ ταῦτα πάσχον παθήματα διὰ.
(Greek text from Platonis Opera, ed. John Burnet, OUP, 1903)
The "earth-born race" are said to have been born wise and happy, as they were fully mature and had no improper memories. Forwards people, such as ourselves, have to learn skills, create governments, etc., and might do that badly. Thus we come back to Plato's exploration of ideal governance.
I would say that Theopompus is a slightly better origin point for individuals magically aging backwards, since Plato's version is about the entire world. In any case, they are not too different in composition time from one another - the two authors were contemporaries.
Erwin Rohde says in his monumental Der griechische Roman und seine Vorläufer that the Meropis story is the oldest "fountain of youth"-type story that he knows (and he cites the Statesman in relation); p222, footnote 1 in the 1914 edition. In that connection, he also points to the Vedic story of Chyavana, who was restored to youth after taking a dip in a specially-prepared pool. That is an instantaneous change of age rather than an example of aging backwards, per the mention in the Rig Veda (7.68) and complete story in the Shatapatha Brahmana (126.96.36.199), which says simply "she took him down to that pool, and he came forth with the age he desired". So although this is centuries older, I don't think it's the same thing that this question is asking about.
Likewise, Herodotus (Histories 3.23) writes of a pool that gives extended life to those who swim in it, but while that's older than Plato it also isn't backward aging. It would likely have been known as a story to Theopompus. Another influence on him would have been the Nostoi, an epic poem of a few centuries prior, which included a story where Medea restored Jason's father Aeson to youth. There are surely many other examples of rejuvenation in older mythology, but I have not found any older reference for gradually aging in reverse, rather than a reset to a younger age.