The myth of the Golden Age is first attested in the poem Work and Days by Hesiod. The core of the poem itself is an agricultural almanac of sorts told by Hesiod to his brohter Perses, and the general theme of it is that of praising and encouraging hard work and piety. It is in this context that the "golden race" of Hesiod is introduced:

First of all the deathless gods who dwell on Olympus made a golden race of mortal men who lived in the time of Cronos when he was reigning in heaven. And they lived like gods without sorrow of heart, remote and free from toil and grief: miserable age rested not on them; but with legs and arms never failing they made merry with feasting beyond the reach of all evils. When they died, it was as though they were overcome with sleep, and they had all good things; for the fruitful earth unforced bare them fruit abundantly and without stint. They dwelt in ease and peace upon their lands with many good things, rich in flocks and loved by the blessed gods.

But after the earth had covered this generation — they are called pure spirits dwelling on the earth, and are kindly, delivering from harm, and guardians of mortal men; for they roam everywhere over the earth, clothed in mist and keep watch on judgements and cruel deeds, givers of wealth; for this royal right also they received; — then they who dwell on Olympus made a second generation which was of silver and less noble by far. ... But when they were full grown and were come to the full measure of their prime, they lived only a little time and that in sorrow because of their foolishness, for they could not keep from sinning and from wronging one another, nor would they serve the immortals, nor sacrifice on the holy altars of the blessed ones as it is right for men to do wherever they dwell. Then Zeus the son of Cronos was angry and put them away, because they would not give honour to the blessed gods who live on Olympus.

But when earth had covered this generation also — they are called blessed spirits of the underworld by men, and, though they are of second order, yet honour attends them also...

Hesiod goes on through the bronze-age, populated by brutally strong men who loved violence and ended up beating each other to death. He continues to the race of heroes; those who were not killed in the Trojan War live on an island in bountiful pleasure, where Cronus (released from his fetters by Zeus) rules over them in eternity. And here Hesiod gets to the point he's been making all along:

Thereafter, would that I were not among the men of the fifth generation, but either had died before or been born afterwards. For now truly is a race of iron, and men never rest from labour and sorrow by day, and from perishing by night; and the gods shall lay sore trouble upon them. But, notwithstanding, even these shall have some good mingled with their evils. And Zeus will destroy this race of mortal men also when they come to have grey hair on the temples at their birth.[5] The father will not agree with his children, nor the children with their father, nor guest with his host, nor comrade with comrade; nor will brother be dear to brother as aforetime. Men will dishonour their parents as they grow quickly old, and will carp at them, chiding them with bitter words, hard-hearted they, not knowing the fear of the gods. They will not repay their aged parents the cost of their nurture, for might shall be their right: and one man will sack another's city. There will be no favour for the man who keeps his oath or for the just or for the good; but rather men will praise the evil-doer and his violent dealing. Strength will be right and reverence will cease to be; and the wicked will hurt the worthy man, speaking false words against him, and will swear an oath upon them. Envy, foul-mouthed, delighting in evil, with scowling face, will go along with wretched men one and all. And then Aidôs and Nemesis, with their sweet forms wrapped in white robes, will go from the wide-pathed earth and forsake mankind to join the company of the deathless gods; and biitter sorrows will be left for mortal men, and there will be no help against evil.

Thus, this is by and large a setup for Hesiod to explain why the world is the way it is, and he goes on after this to pontificate about proper conduct and the consequences of it:

Neither famine nor disaster ever haunt men who do true justice; but lightheartedly they tend the fields which are all their care. ... But for those who practise violence and cruel deeds far-seeing Zeus, the son of Cronos, ordains a punishment.

Hesiod is clearly not much concerned with explaining the nature of the golden or silver men or why they were made the way they were, or why there were only a generation of each. What he's interested in is using them as a contrast to the way the world is now. For instance:

Wealth should not be seized: god-given wealth is much better; for if a man take great wealth violently and perforce, or if he steal it through his tongue, as often happens when gain deceives men's sense and dishonour tramples down honour, the gods soon blot him out and make that man's house low, and wealth attends him only for a little time.

Recall how the heroes who went to war to plunder wealth died, but those who did not were rewarded with eternal bountifulness on an island at the end of the Earth.

The work also abounds with drawing on earlier Indo-European tradition, e.g.:

The eye of Zeus, seeing all and understanding all, beholds these things too, if so he will, and fails not to mark what sort of justice is this that the city keeps within it.

Compare this to the late Rgvedic hymn to the sun (Rv 10.37):

1. Do homage unto Varuṇa's and Mitra's Eye: offer this solemn worship to the Mighty God, Who seeth far away, the Ensign, born of Gods. Sing praises unto Sūrya [the sun], to the Son of Dyaus [the daylit sky, cognate with Zeus].

Mitra and Varuna are the vedic deities that keep track of oaths and covenants and punish the breakers of them, and the sun as the eye of a watchful deity is recurring in Indo-European myth. Another itneresting parallel is that Hesiod at the start of this section says

Or if you will, I will sum you up another tale well and skilfully — and do you lay it up in your heart, — how the gods and mortal men sprang from one source.

While I don't find it wholly clear how Hesiod conceptualizes this "one source" (because the gods made the mortal races, after all) this can be compared to the myth retold in Rgveda 10.90 of the primal giant Purusha:

3. So mighty is his greatness; yea, greater than this is Purusa; All creatures are one-fourth of him, three-fourths eternal life in heaven.

In any case, this poem is simply not very concerned with any connection between the rule of Cronos and the Golden Age. The first two ages are said to be the creation of "those who dwell on Olympos" whereas the last three are explicitly the creation of Zeus, who is also identified as undoing the Silver Men owing to their impiety. Zeus is frequently identified as "the son of Cronos", but I suspect this is mostly just for the purpose of poetic meter. The point Hesiod appears to be making with the Golden Men is that they were blessed by the fruits of the earth:

and they had all good things; for the fruitful earth unforced bare them fruit abundantly and without stint.

, and that to attain good in the present age, one must work hard so that the earth will bear fruit, tying into the overarching agricultural theme of the poem. With the Silver Men, the theme is the danger of impiety:

nor would they serve the immortals, nor sacrifice on the holy altars of the blessed ones as it is right for men to do wherever they dwell. Then Zeus the son of Cronos was angry and put them away, because they would not give honour to the blessed gods who live on Olympus.

The third and fourth ages illustrate the ignobility of seizing wealth by force as we have discussed, and in the present age, one must take lessons from all of these, which basically means working hard and minding one's own business:

Work is no disgrace: it is idleness which is a disgrace. But if you work, the idle will soon envy you as you grow rich, for fame and renown attend on wealth. And whatever be your lot, work is best for you, if you turn your misguided mind away from other men's property to your work and attend to your livelihood as I bid you. An evil shame is the needy man's companion, shame which both greatly harms and prospers men: shame is with poverty, but confidence with wealth.

It is in this context also worth pointing out that Cronos (and more so his Roman counterpart Saturn) seems to have continued playing some role as a patron deity of the harvest (recalling his sickle), being the subject of the Attic festival of Kronia. Moreover, in the context of Interpretatio Graecia, in spite of his obvious character flaws in the Theogony, Cronos was still identified with patriarchal deities, such as the Canaanite El. We should in general not assume that there was any one, singular understanding of a deity like Cronos, in spite of the obvious influence of the Theogony.

Finally, it is worth noting that Hesiod actually tells two, later conflated, tales of how the toils of the present day came to be in Work and Days - he first tells the myths of Prometheus and Pandora, concluding it with,

So is there no way to escape the will of Zeus. Or if you will, I will sum you up another tale well and skilfully — and do you lay it up in your heart, — how the gods and mortal men sprang from one source.

before he continues into the myth of the ages. No doubt Hesiod must have drawn on many different oral traditions for his poems, which would not all have been free from contradiction.