If you knew why multi-generational poverty existed you would win a Nobel Prize and who knows what else.
No one has been able to figure this out so far, and what you wrote above is not necessarily even a good description of what multi-generational poverty looks like.
Well, given that UBI studies have been promising so far (despite their limitations), there seems to be a decent chance that quite a lot of multi-generational poverty is primarily caused by... multi-generational poverty, meaning it's a self-reinforcing cycle that's difficult for people to escape. Or in other words: when you're broke, it's really hard to build wealth, so you're likely to stay broke.
Perhaps it's an over-simplification, or perhaps a lot of people have been over-complicating the problem, particularly when they're trying to prop up a pet political bias.
If we implement UBI on a large scale and it drastically increases upward mobility, I suppose this hypothesis will be more or less proven. I hope that day comes sooner rather than later so we can find out.
No one has been able to figure this out so far, and what you wrote above is not necessarily even a good description of what multi-generational poverty looks like.