Hesiod is mixing two quite distinct stories: the Titans and their war with the Olympians, and the Myth of the Races (not 'ages') were originally totally separate things. The Myth of the Races isn't part and parcel of the make-up of Greek myth in the same way that the Titanomachy is: the story existed, obviously, and some later poets borrowed from Hesiod, but it had no role in Greek religion, or folk narratives, or in generating mythical narratives around itself. The war of the Olympians and Titans does do all of those things.

Put simply, the Titanomachy is baked into Greek myth; the Myth of the Races is an intruder, consciously adapted from Near Eastern literary models.

The Titanomachy plays a role in Greek religious beliefs, notably in Orphic religion; it generates stories like the acceptance of divinities from the Titans' generation into the Olympian regime, such as Hekate, Dione, and Hyperion; and it's framed around the idea of Titans as chaos divinities, while Zeus and his brothers bring order to the cosmos.

The Myth of the Races, by contrast, is borrowed from a literary tradition that equates various metals with ages of the world, with parallels in the Sumerian Lagash king list and An = Anum, the Hebrew books of Daniel (and to a lesser extent Genesis), the Iranian Avesta, and the Indic Laws of Manu and the Mahabharata.

Just to illustrate, here's a snippet from the Lagash king list (tr. J. A. Black):

In those days a child spent a hundred years in [?nappies?],
spent a hundred years in his rearing.
He was not made to perform (any) assigned tasks.
He was small, he was feeble/stupid, he was [with] his mother.

And here's a bit from Hesiod's account of the Silver Race (tr. Glenn Most):

A boy would be nurtured for a hundred years at the side of his cherished mother,
playing in his own house, a great fool [nēpios: more literally 'infantile, toddler-like'].

No extant Sumerian sources give the series of metals that we get in Hesiod, but these passages indicate a close relationship. And here's a bit from Daniel chapter 2 which covers the full range of substances --

... 32 The head of that statue was of fine gold, its chest and arms of silver, its middle and thighs of bronze, 33 its legs of iron, its feet partly of iron and partly of clay. ... 36 This was the dream; now we will tell the king its interpretation. 37 You, O king, the king of kings ... you are the head of gold. 39 After you shall arise another kingdom inferior to yours, and yet a third kingdom of bronze, which shall rule over the whole earth. 40 And there shall be a fourth kingdom, strong as iron; just as iron crushes and smashes everything, it shall crush and shatter all these.

Here the metals act as allegories for historical dynasties -- the Neo-Babylonians, Medians, Persians, and Macedonians ('partly iron and partly clay' referring to the Ptolemies and Seleucids).

The literary genre of the Hesiodic Works and days, as 'wisdom literature', is adapted from Hittite and Levantine models, and the Sumerian texts are by far the earliest, so it may be that Mesopotamia or the Levant is the ultimate origin of the Myth of the Races. There's a lot we don't know, of course.

Here are a few older answers of mine that deal with similar themes, and give some bibliography: on the Myth of the Races, one and two; and on the Titans and how they're baked into Greek myth. M. L. West's book The east face of Helicon (1997) has a good section on the Myth of the Races at pp. 312-319, and his Indo-European poetry and myth (2007) has a section on 'upper and lower gods' at pp. 122-124.