Maybe it's wrong and I'd love to know if that's the case but from personal experience the only way I've seen out of poverty is interest in an in demand field leading to the building and maintenance of marketable skills that allow you to earn a living sufficient to attain economic escape velocity. That seems to me to be a whole lot do with luck at the ground floor. And fiscal and social policy can be as much of a burden as it is a boon all the way along the pipeline.
That said, that escape velocity was directly mediated by both the tax burden of the jurisdiction coupled with the economic opportunities of the jurisdiction and at the end of the day it meant the correct choice was to leave for greener pastures, both lowering the necessary target for escape velocity as well as reducing economic drag getting there.
In the meantime all those kids I knew back in the old neighbourhood are still there, mostly on subsistence handouts, firmly in poverty, and show no signs of that changing.