Like I said, it's definitely possible if you haven't gotten yourself into debt or had criminal problems or suffered medical issues or made any enemies.
But every one of those ways out requires you to be lucky and continue to avoid all three of those problems, which gets markedly more difficult when you are poor, and not everyone is lucky. you've admitted yourself that succeeding when poor basically requires you to break the law, and while most of those probably won't result in a criminal record, they certainly can if someone with a bit of power decides they don't like you.
There is only one relatively quick and fairly reliable way out of poverty - that is, to sign yourself into slavery by taking out a whole heap of debt and invest it into supporting yourself while building your skills in the hopes you can get a better job. (The route I took, by taking out big-time student loans to go to state college - even though my grades were good enough to get a scholarship and I worked through the experience while living out of my car or cheap apartments with no heat or electricity, I still ended up with quite a bit of debt. I could have done better, but it would have required me to know about the better options, which isn't exactly easy)
And that seems less likely to succeed as time goes on, and you're usually gambling with limited knowledge to accomplish even that.
There are ways out of poverty, a lot of them are non-obvious and it's entirely up to you to figure something out.
If you've been in poverty for a while, your resources for "figuring them out" are pretty limited. A lot of people in poverty don't even get the government assistance that might help them because they honestly don't know about it. I think education, free and widely available and made obvious to those who need it, is one of the best uses of our government we could use to help the poor. There are ways out of poverty - most of them hard, none of them guaranteed, the best all but unknown to those who could best make use of them - but they exist.
Saying "they'll just have to figure it out on their own" is pretty simplistic, because there's always going to be a lot of guesswork when you're operating from such a disadvantaged position, and mistakes are costly.