Best answers I could find: https://www.reddit.com/r/AskHistorians/comments/1pw0un/were_the_titans_the_gods_of_a_pregreek_society/
In short, likely no, but what we do have is evidence of similar mythological elements across indo-european cultures.
Either this trope has evolved from a common belief, or much more likely, it represents a fundamental human motif of new traditions supplanting the old; something older than history itself.
Yes, Titans were worshiped even in the "later" years.
There were festivities for Cronus in Olympia, Elathion and Athens, as also Rhea was quite prominent through her cult of Cybele.
ἔστι δὲ ἀρχαῖα ἐν τῷ περιβόλῳ Ζεὺς χαλκοῦς καὶ ναὸς Κρόνου καὶ Ῥέας καὶ τέμενος Γῆς τὴν ἐπίκλησιν Ὀλυμπίας - Pausanias 5.20
Helios (Sun) was worshiped in Rhodes through his cult, and one of the seven wonders, [Colossus] was dedicated to the Titan.
Prometheus was worshiped by humans also for giving the gift of fire, even Aphrodite (Venus) who is considered an Olympian Goddess, was technically a Titaness. For sure though they were not near as popular as the Olympian Gods, and it is assumed that they were basically worshipped more out of fear than preference.
(https://en.wikipedia.org/wiki/Colossus_of_Rhodes)
also if you are interested, /r/mythology is a small but helpful subreddit on these kinds of topics.
In short, there exist theories and possibilities that Titans were worshipped pre-Greek, but there lacks enough evidence to really say. While it is possible, also consider that older gods were adopted by Greek society. Some of the major Olympian gods such as Artemis are thought to have been from pre-Hellenic worship.
Side question:
One of my favorite theories is Euhemerism - that ancient gods were based on Prehistoric Kings whose stories were exaggerated over the centuries until they became larger than life figures. Unfortunately I don't have much information on this topic. Off the top of my head, I know that Asclepius seems especially suspicious because of his decidedly non-divine appearance in The Iliad, and the fact that he is missing from Hesiod. Likewise, it seems like some historical figures like Alexander might have eventually became gods, if it weren't for the fact that writing existed. And as a result, there was factual evidence left behind which confirmed that he was a man, which made it harder for the truth to become warped over time.
But anyways, besides minor facts like these, I don't have much information on this subject. Do you know of any other evidence to support this theory?
To expand on OP's question, is there evidence that the Titans were a relic of an earlier system of gods that were supplanted by Olympian worshipers?
Not an answer, just kind of an additional question.
Wasn't the mythology of titans based before creation? I don't remember much discussion about Greek creationism, but I remember there not being a lot of structure before Zeus, Hades, and Poseidon.
So I guess a question of my own would be what the creation of man/earth was in Greek religion/mythology?
Side question about mythology. How did the greeks view the Titans vis a vis the gods? from a literary perspective they just seem to be another generation of the same sort of entity. Was it just one dynasty falling to another, or was there some fundamental difference in their nature?
Also I recognize that mythology is a lot like comic book canon, everything is different based on when you are talking about.
I'll answer best of my knowledge with what I know with Socrates. During thistimeAthenian politicians followed Helios and other deities. Socrates was challenging the people at the center on critical thinking on the Gods and the tyrants who rule them. He was then put on trial for corrupting the youth.
Sorry, are you asking in the second question whether people in Greek mythology worshiped Titans, or whether people in real life worshiped Titans?
Because if it's the latter I think I'll have to look up Pelasgians and other pre-Greek civilizations of the Greek peninsula, because (correct me if I remember wrong) they were the prime worshipers of the Titans.