I have located an early Christian discourse in which Satan is explicitly linked to the Titans, possibly to Typhon by extension. Both the Christian Origen of Alexandria and the pagan Celsus agree on the myth of the Titanomachy as the basis of the myth of the Fall of Satan.
Celsus, as quoted by Origen, accused Christians of impiety by posing an adversary to God - that being The Devil, or rather Satan. Celsus argued that Christianity poses a God that desires to do good but is helpless to do it because he has someone (Satan) counterveiling his will. Then, Celsus discusses ancient mythology concerning war among the gods. He focuses specifically on a myth told by Pherecydes of Syros, in which in the gods Kronos and Ophioneus raise their armies against each other in a battle to determine who will rule the cosmos.
At this point we need to step back a bit. Ophioneus, or Ophion, is the name of a serpent deity who seems to represent the forces of chaos. In some myths, Ophioneus is presented as the first divine ruler of the cosmos, though Pherecydes doesn't agree with that. As for Kronos, it is possible that in Pherecydes' myth this refers to both the Titan Kronos and Chronos the personification of time. The two figures are not traditionally conflated with each other, but it seems that Pherecydes probably did interpret them as being the same deity. In Pherecydes' myth, Kronos and Ophioneus battle each other before the ordering of the cosmos begins, though the full account of this battle is not entirely clear. Celsus believed that the loser of this battle, Ophion, was cast into the ocean (or rather Oceanus).
Some fragments seem to support the notion that it is Oceanus rather than Tartarus that Ophion is cast down into. But Ophioneus seems to also be considered identical or parallel to Typhon, who, in Greek mythology, was cast down into Tartarus or under Etna after his defeat by Zeus. It is possible that Ophion may have been thought to be born in Tartarus, which Pherecydes depicts as a cave below the earth, whereas Typhon was also born in a cave as the son of Gaia (earth) and Tartaros.
One thing to note is that, for Pherecydes, unlike many other ancient cosmogonies, it seems there is no primordial chaos that precedes an act of primeval demiurgy resulting in cosmic order. Instead, the forces of order and chaos existed besides each other forever and in conflict. For Pherecydes there was also no creation out of nothing. Instead, three gods were the first to exist all along: Zas (Zeus), Chthonie (Ge/Gaia), and Kronos/Chronos. He believed that these gods existed eternally, and that Chaos somehow came to be with no explanation.
Anyway, Celsus brings up Pherecydes' myth while discussing the concept of Satan, and then says that the Greek myths concerning the Titans and/or the Giants, and the Egyptian myths concerning Typhon (obviously meaning Set in this context) shared a similar symbolic meaning. He also relates that Hepheastus told Hera that he once felt the might of Zeus and hurled down from Olympus, and that Zeus boasted to Hera of how he bound and hung her in golden chains and hurled all the gods who opposed him from Olympus, as if to relate these to the Fall.
Celsus then does something interesting: he identifies the words of Zeus to Hera with the word of God to matter, arguing that this signifies matter that was originally was in discord before God then took and bound it together and arranged it with law, and then banished disorder. Demons who create disorder in the cosmos are related in Celsus' analogy to Titans and rebelling gods: they are chastised and hurled down. Tartarus, according to both Celsus and Pherecydes, is the place where Zeus banishes disorderly or insolent gods: in a word, prison.
Origen seems to actually agree with this analogy. In fact, in Book 4 of Against Celsus, Origen referred to "earthly demons, who delight in frankincense, and blood, and in the exhalations of sacrificial odours, and who, like the fabled Titans or Giants, drag down men from thoughts of God". Moreover, Origen argued that the writings of Moses mentioned a "wicked one" and his "falling from heaven" before the time of Homer and Pherecydes. Origen believed that Satan was the serpent that tempted Adam and Eve and that this was the original myth behind Ophioneus. If Origen interprets Satan as Ophioneus, then I would argue that he implies this connection for Typhon, and the Titans and Giants in relation to his demonic host. Origen also says that Satan is the "destroying angel" and the scapegoat Azazel.
This is interesting to consider in light of Plutarch and other sources whereby Typhon Seth is represented as a sacrificial animal. For Plutarch, Typhon is destined to never be completely defeated, and his power resides in the sacrificed animals and their slain blood, which, for Plutarch, ultimately nourishes the cosmos at least in the act of sacrifice, which pleases the powers of Osiris and Isis.
In any case, Origen seems to agree with Celsus on the Titanic-Satanic analogy, with the difference being that Celsus thinks the Christians were simply imitating pre-Christian myths while Origen thinks the Christian narrative preceded those same myths.
It might be worth noting that 2 Peter 2:4 says that God did not spare the angels who "sinned" against him, and that he threw them into "the pit". This is sometimes rendered as "hell", but in the Greek New Testament "the pit" is translated as Tartarus. Yes, none other than Tartarus, the prison of the Titans, and perhaps of Typhon and Kronos. From the pagan (or at least Celsian) standpoint at least, the parallels could not be clearer than this.
