The present day "immigrant" influx to Europe reminds one of how the Goths, fleeing the Huns, sought to enter the Roman Empire, and it's aftermath.
but an earlier puzzle is the Bronze age collapse and the invasion of the Sea Peoples.
Ah but the invasion happened in two periods, the first with the Pharoah who followed Ramses the Great of bible fame, and the second with Ramses III, who is best known for winning the battle but bbing assasinated by his wives after coming home.
There is some question if this was done for greed, or if he neglected his own people from famine.
Well, anyway, Maritime History podcast is covering those times in their recent podcasts LINK
I always wondered if the raid on Egypt in book 14 of the Odyssey (which was actually Ulysses telling tall tales as usual) was actually a rememberance of other Greeks who raided Egypt...
However, the second wave is the real question: Were they the cause or the result of the Bronze age collapse.
and modern archeology notes that the Philistines might have included many Mycenaean age Greeks.
if a lot of this sounds confusing, it might be me, or it might be because the specialists are still arguing about the details
Eric Cline in his book 1177 has a discussion of the controversy,