OK, let's do some math. The minimum wage in Portland is over $11/hour, but let's use $10/hour. If you work 30 hours a week at $10/hour, you'll get $300/week and a little over $1,200/month. You'll pay at least $200/month in taxes, so let's say you get $1,000 just to keep it a round number. That's easy enough.
OK, you're poor. You'll need a roommate. Patty and I lived in a 550 sqft apartment (what all my friends called the crappy little apartment) for 5 years just a few years ago. Yes, we were a couple and it was small, but we survived just fine. It was in Portland and I paid about $650/month for it. Split that by 2 and you get $325/person for rent. That leaves you with $675. The electric bill will cost you $75 max per person. That leaves you with $600. You'll need phone and internet. My smartphone plan with 3GB of data costs $40/month. That leaves you with $560. Maybe you each pay $50/month for internet/tv. That leaves you with $510.
Food is going to cost you at least $200/month. Let's call it $250. That leaves you with $260.
Transportation. Well, bicycles work just fine. I've riden my bicycle for 40 miles a day through hills, rain, snow. You'll be in shape. It's fun. Once you have the bicycle, it's basically free. You can get a decent bike on Craigslist for $200. Let's just say you figured out how to get a bike and transportation is free.
OK, you're surviving. You're only working 30 hours a week and you have $260 left over per month. You'll need it for clothes and a little entertainment. You still have plenty of time to use that internet connection to educate yourself into a real career.
This is how I lived when I was 19, 20 and 21. I studied music 6 hours every day. I was in shape and healthy. There's definitely motivation to move up the ladder. You probably don't want to spend your whole life doing this.
I think the best solution to help these people is passing a law that makes it illegal for an employer to require you to have a college education. If you are working hard at home schooling because you don't want to work fast food for the rest of your life, you shouldn't be discriminated against because you didn't have the money to pay for college.
I favor increasing the minimum wage, I just don't see it as a huge prioritiy like climate change. Having a path out of poverty like what I was talking about is the best action for fighting poverty in my opinion.