The mythological scenes depicting the war of the Olympian gods vs the early more beastly Titans to me always represented the Greeks giving up or rejecting the earlier gods who were half human and half monster like found in earlier civilizations in Mesopotamia and Egypt and embracing anthropomorphic gods - gods that looked and acted like men.
There were a number of traditions more or less coexisting, which was also the case in Egypt (the consolidated beliefs there were a terrific mishmash as a result), Mesopotamia (and neighboring territories such as Elam), and Europe (which indeed Greece was part of) due to the occasional ingress of big migrations coming out of central Asia down the steppe. The need to make disparate traditions whole (probably for political reasons, unions of towns under one rule, that kind of thing) led to unusual genealogical myths (Venus from the head of Zeus, Apollo from Zeus bangin’ a swan, for that matter, Kronos devouring his children, Ouranos getting castrated, etc). Apollo is actually not originally Greek at all (not even his name), and yet became in some ways the quintessential pagan Greek deity.