You said: "Some do [make any significant improvement], but it's a small percentage."
I posted the fact that 43% start and stay in poverty, but that means 57% get out. 57% is not "a small percentage".
Even using your new data source of "and 70 percent remain below the middle." (which is counter to your original claim that people stay stuck in poverty - you could still remain below the middle, but not be in poverty any more), that still means 30% make their way out, which once again, is not "a small percentage".
"Plenty of immigrant families leave low opportunity nation states and work what you consider demeaning work whilst taking steps to ensure their children seek more aspirational jobs and careers."
Nothing you posted indicates that's not a small percentage of people. But it certainly does show that growing up poor is a huge obstacle, and that while upward economic mobility does exist in the US, it's quite limited. To me, that all points toward favoring UBI, and against the idea that people can reliably escape living paycheck to paycheck (or worse) just by developing a good work ethic.
Also, it's not "my new data source". It's your data source. You just didn't bother to reference it.
Though I have no idea where you got it from, or whether it refers to one country or the whole world, getting out of the bottom 20% and ending up the in the bottom 30%, for example, would still leave you in a situation where you're struggling to get by in most countries in the world. Which is why this doesn't contribute much without more context.
Edit: found it - https://www.pewtrusts.org/~/media/legacy/uploadedfiles/pcs_a...
It's quite interesting that you left out the very next phrase, cutting off your quote in the middle of a sentence:
"Forty-three percent of Americans raised in the bottom quintile remain stuck in the bottom as adults, and 70 percent remain below the middle."
Also, right above that is:
"Americans raised at the bottom and top of the family income ladder are likely to remain there as adults, a phenomenon known as 'stickiness at the ends'."
No wonder you didn't post a link.