There's a flip side to this question, which you may want to consider:
https://cauf.substack.com/p/weapons-of-mass-migration
TL;DR - I think you're asking the wrong question. Mass migration is rarely organic, it is usually in direct response to some major event (e.g. the volcanic winter of 536 AD, kicking off the early mediaeval migration period, which Cauf didn't mention), or outright directed by governments (like all the ones he did).