Oh boy, one I can actually point to a legit answer to for someone in this thread.

It's way too long for a comment, but the TLDR is:

Ramses II captured twelve groups of Anatolian tribes following Kadesh, one for each son with him.

After Ramses II is dead, at least one of those tribes (the Lukka) are fighting in a one day war against his son Merneptah alongside other sea peoples (this is the first connection between these tribes and the sea) and Libya. Notably, a number of the sea peoples in this battle were oddly recorded as being without foreskins.

You actually see this event in Homer, when Odysseus tells about a one day battle immediately after Troy against Egypt where he is taken captive, parties in Egypt for seven years until a "certain Phrygian" shows up and tries to ransom him to Libya.

Seven years after that one day battle against Merneptah is when the usurper Amenmesse (referred to as Mose in Papyrus Salt 124) takes Egypt for 3 years.

Ramses III talks about the end of the 19th dynasty as having been characterized by the city governors making decisions and the gods having been made like men. Both fairly Phonecian features, given the city state governance and the euhemerism of the Phonecian mythos reported by Philo of Byblos from around the time of the Trojan War.

Ramses III later claims to have forcibly relocated the sea peoples into the Levant, though as can be seen in places like Ashkelon they'd already conquered and set a foothold there as well.

In particular, there was supposedly a commander named Mopsus/Muksus who had conquered Ashkelon, and who you later see the rulers of the Denyen sea peoples in Adana crediting their ancestry to in 8th century BCE bilinguals.

Do any of these features maybe ring some bells?

Twelve tribes? No foreskins? Captured into Egypt?

How about a bunch of pre-Greek peoples sailing around the Mediterranean on ships?

Part of the problem is that the surviving oral histories of this period seem to have underwent extensive reworking, with a particular focus on ethnocentrism such that the Argonautica is solely about Greeks and the Biblical Exodus is only about Israelites.

The two stores share surprising details, like how in the Argonautica the prophet Mopsus died as they wandered by foot back from a battle in North Africa, similar to how the prophet Moses died in the desert as they were wandering by foot back from North Africa. In fact, right after this happens in the Argonautica it tells of a local sheepherder killing one of their elite warriors with the cast of a stone, similar to the Biblical story of a sheepherder killing an elite sea peoples warrior with the cast of a stone (thought to be reappropriated into the Davidic story but not originally about him).

In fact, one of the two ways of Hellenizing the name Joshua is Jason.

A problem was Homer's combining the Mycenaean conquest of Anatolia with the later retaking of Wilusa from the Hittites screwed up all the later Greek chronologies (depending on the sources, Perseus is his own ancestor), so the Greeks thought their Argonautica period was before Troy.

But after the conquest of Alexander, when multiple cultural sources were all being considered together, you had scholars suddenly realizing they were looking at shared history, such as Atrapanus of Alexandria having Moses on the Argos teaching Orpheus the mysteries, or Hecataeus of Adbera's version of the Exodus story that had multiple different peoples all being exiled from Egypt, including the Phonecian Cadmus or Libyan Danaus.

Some of those stories have remarkable overlap to this period too, despite their late character. For example the story of Danaus, Lybian brother to the Pharoh with 50 sons who later becomes leader of the Greeks, is pretty interesting in light of Ramses II's forensic report describing him as appearing like a Lybian Berber given he had 48-50 recorded sons. You have oddities like Herodotus's crediting the multi-day women only Thesmophoria festival to the daughters of Danaus fleeing Egypt, and you have a reference to a multi-day women only ritual in Judges 11 where it's explained with what's effectively the story of Idomenus's return home from the Trojan War.

The problem is that even myth which contains kernels of truth also contains lots of kernels of BS, and between survivorship biases and anchoring biases, the picture of these periods is extremely muddied. Just look at how little attention the Greek and Egyptian accounts of the Exodus narrative get from scholars relative to the amount of attention the Biblical version gets.

Archeology may gradually help. For example, Yigael Yadin's theory that the Denyen sea peoples were the lost tribe of Dan given the reference of Dan "staying on their ships" in Judges 5 may be strengthened by the recent discovery of Aegean style pottery made with local clay in Tel Dan.

This theory is particularly interesting given the "House of Mopsus" of the Denyen relative to the story in Judges 18 where a descendant of Moses becomes the priest for the tribe of Dan contrary to all the stuff about how it needs to be a descendant of Aaron. As well, you can see in Ezekiel 27:19 where Greece and Dan are trading together with Tyre, with the goods mentioned as in line with Adana's relative geography. The Denyen and the neighboring Ahhiyawa might be a good fit for who was being referred to here, and given the exact same form for Dan as when mentioned as staying on their ships, the Denyen become a compelling match for the tribe.

Another interesting archeological detail is the imported bees from Anatolia in 10th-9th century BCE Tel Rehov.

My broad guess looking at the many different accounts was that the various peoples brought into Egypt under Ramses II had Merneptah either exile foreigners or deny previous land rights to them after he took power, which led to the Lybian war. After losing that, the surviving tribes (who had greater allegiance to each other and reclaiming a home in Egypt as opposed to individual countries of origin) went back and conquered much of their homelands in what were effectively populist uprisings (conveniently often at times of destabilization from famine and natural disaster) raising enough of an army doing so they were able to successfully take all of Egypt a few years later. They ultimately couldn't hold it, left and continued to conquer areas of the Mediterranean until finally becoming fractured enough a generation or two later that they were beaten by Ramses III and individual tribes kept extremely fractured and partial retellings of the events which took on increasingly mythical form as time went on and changed specifics as power dynamics shifted or the myths were absorbed into other cultures.

Give it another 20 years or so, and I think you'll have a lot more of an official answer to your question than you might have previously expected to end up with. There's enough there, particularly in light of recent archeology, that I doubt the status quo collective shrug will hold much longer.