Perhaps UBI on its own is not sufficient to give hope for a better future, but combined with affordable education maybe it would be?
I imagine if one could take some time off without fear of starvation (or going massively into debt) to raise one's skills, then upward mobility would be much more accessible. I don't know if UBI is the only solution but I can see how it would at least solve part of the problem.
I'm too young to have experienced it myself but my understanding is that there was a time when people could actually survive off jobs which didn't require a college degree. I don't think this is possible in most places anymore and given that college tuition has only increased, it seems like upward mobility has decreased.
I realize that college isn't necessarily the right path to upward mobility but I think you can generalize the argument to most forms of education and it would still apply.