The short answer is that we don’t know and can only make a calculated guess that at least largely they were not Pre-Greek gods but a later import or invention. If they, or some of them, were the main gods of a Pre-Greek religion, or a compilation of some, we just know too little about the pre-Greek groups, and even their languages have barely survived: the Minoan of Crete is undeciphered and we can just about take a stab at its syllable structure (maybe...), Lemnian (if truly ‘pre’-Greek) is just about barely partially understood from two fragments, and as for the pre-Greek languages of the rest of Greece we have no idea.

However, though the etymologies of some Titans is disputed, including Cronus and Rhea, several of them have definitely Indo-European and Greek names: Phoebus, Hyperion, etc. These could have been translations, but this already raises questions as to what remaining attributes they had that would tie them to anything previous. If they were Indo-European, then the fact that Zeus Pater descends from the name of a major Indo-European god (appearing in Roman Jupiter and even Hindu Dyaus) casts a little doubt on their being pre-Greek, and it’s worth noting that many pre-Greek toponyms and even names for flowers and such things indigenous to Greece that the Indo-Europeans might not have encountered were preserved, so the lack of definitively pre-Greek names is odd if they were: that said, some aren’t definitively explained.

As for what the Greeks may have recorded, anything that relates to the ‘Pelasgians’ and other pre-Greeks is shrouded in the constantly evolving and often contradictory mythology itself.

We have nolittle record of dedicated cults to any particular Titans from the classical era. EDIT: This was a presumptuously strong statement of mine. There is at least one mention of a cult to Cronos - see u/PoisonMind’s comment below.

But we can get some clues by looking at the myths themselves, and other myths from the region. They appear in detail in Hesiod’s Theogony, arguably the largest source of ‘pre-Trojan War’ Greek myths, and otherwise the main Titans whose stories are fleshed out, rather than appearing in a list or genealogy, are Cronus, Rhea, and Iapetus. Traits or ‘roles’ are also given to Mnemosyne (memory, which her name means) and Oceanus (who represented the world ocean encircling the known world). ‘Secondary’ Titans not included in Hesiod’s list most famously include Prometheus, whose story as thief of fire is a common trope in ancient mythologies of the region (and all over the world), and Atlas (who holds up the world).

Otherwise, they seem to be tied to their children, and in fact the list of the generation of 12 ‘main’ Titans (the ‘main’ series of children of Uranus and Gaia) squares against the list of 12 Olympians (children of Cronus and Rhea) seems like a post-hoc construction and the Titans show more evidence of being ‘filled in’, rather than the other way around.

For example, Hyperion - meaning ‘the one above’ - is a poetic term used by Homer for the sun or sun god, but Homer uses it in a context during the time of the Trojan War rather than before the Titanomachy. It seems that the separate name may have been used to fill in the list for the previous generation. After all, he does not appear as a separate entity in Homer, and his name is very much Greek.

On the other hand, the names of some Olympian gods have also been attributed to a Pre-Greek substrate, especially by Beekes, though I think all of these have rival theories of coming from either corrupted Greek roots or later Anatolian or other loans.

Another possibility, which I find more compelling, and espoused by Hard and Rose in their ‘Greek Mythology’, is that they are based on Mesopotamian series of ‘former gods’. The Anunnaki (now with unfortunate associations with David Icke, alien conspiracy theories and whatnot) were a previous generation of Sumerian gods who were overthrown by a new generation of gods and by the Akkadian and early Assyrian period locked in the underworld by their new ruler. This idea seems to have spread from Mesopotamians the Hurrians and Hittites, and the Anatolians both influenced and feature prominently in Greek mythology - or maybe it descended from an even older, in which case necessarily prehistoric, religion. So although the story does ‘sound suspiciously’ like an in-universe or diegetic mythologisation of the actual overthrow of a former religion - and it may well derive from that, we have no way of knowing - even if true it may not have happened directly in Greece, but as a Semitic (Akkadian/Assyrian/Babylonian) ‘overthrow’ by Marduk or others of the Sumerian gods, or even within some other culture, and then that ‘former divine generation’ idea itself may have been imported by the Greeks. This, to me, seems more likely.

As a side note, there are several parallels of the general phenomenon which don’t appear to be related as well, including in Norse mythology: the Æsir and Vanir are described as separate pantheons, and the incorporation into one religion is speculated to be the result of different religions coming to terms. Similarly, Hindu mythology includes multiple layers of gods: the Indo-European Dyaus Pitr barely gets mentioned in the Vedas, which focus more on the ‘Vedic’ gods like Indra with a bare mention of Vishnu, and now the more popular gods today are the likes of Shiva, ‘modern’ Vishnu and his avatars (one of whom defeated Indra in a famous story), Hinduism has discrete incidents of such incorporation, but with a stronger tradition of identifying them by different names, manifestations or avatars of the same gods (eg Shiva and Vedic Rudra, Rama and Krishna - and even Buddha - as avatars of Vishnu, etc.). And then way back you even the rival devas and asuras, whose Zoroastrian cognate daivas and Ahura seem to have ‘reversed’ roles (though the most simplistic theories of how this came about from a basic religious rivalry have been largely dismissed). Changes in beliefs and worship being reflected in the mythology itself is a common phenomenon in mythology around the world.

Unfortunately, a lot of all the exact details of this is, and at this point has to be, speculative, and in the end we simply don’t know.

There may of course be further answers, but /u/KiwiHellenist covered the differing approaches to this question in this answer a few months back – looks like OP deleted the question so it's no longer easily searchable.

OK completely tangential side-question by some guy who isn't even the OP, but Goethe in his letters discussing Faustus II mentions an alleged ancient city in Sicily, called "Engion", which apparently had a matriarchal cult, and was the inspiration for that infamous quote about Faustus and Mephisto descending into "the realm of the mothers".

He claims to have read about that city in some actual ancient source. Is there any truth to that? Is there even a mention of any "Engion" and it peculiar matriarchal cult anywhere?