When unemployment is high, it is the unemployed who are bidding for jobs, thus incomes fall.
When unemployment is low, it is the employers who are bidding for employees, thus incomes rise.
Minimum wage is, at best, a temporary sugar rush for a few years until it needs to rise again; or, at worst, a job killer that shuts down businesses, increases prices, and reduces the choice of goods and services available to us.
The real way to increase incomes is to bring down unemployment. Here's Walmart advertising for jobs in Williston, North Dakota (In Williston, the unemployment rate is 0.9%. USA national average is 6.1% according to official statistics):

Employers in Williston do not advertise jobs at, or near, minimum wage, because they'd essentially be laughed out of town.
I'm currently living in the UK (about to emigrate to Hong Kong in a few weeks), I've just finished University. While at University, I had to work part-time at McDonald's - my parent's income is too high for me to receive additional benefits from the Government, and my parents fundamentally believed that my education is my investment, and not theirs (I don't necessarily agree with this, but that's their decision to make).
McDonald's paid me minimum wage. I didn't care much about this. It's what I was worth to them. And here's why: the manager told me that, on any given week, their one store would receive at least 50 unique job applications. It hires about 1 or 2 individuals per month. Everybody knows the job is minimum wage, and yet still 50 people per week want to work for it. Incidentally, there's a second McDonald's in the centre of the city which apparently receives even more job applications.
Incidentally, in line with the whole career thing, my managers at McDonald's loved me, as I always worked hard, had a smile about my face, and genuinely enjoyed my job. Before I left, they were training me up for a promotion. Wage increases in places like McDonald's are actually fairly dramatic, after 2 or 3 promotions in as many years, it's quite easy to be on double minimum wage.
As for my move to HK, I'm a fresh graduate, but I did an internship at a major bank a few years ago, and now they want me back. I wasn't on a huge amount before, but it was livable. I'm going back to close-to-triple the amount I was on before, on the understanding of a steep career path.
Get in early, work for low amounts, work hard, and constantly increase your value. Education doesn't stop when you finish highschool or college, it needs to continue throughout your entire life, otherwise you'll likely just tread-water until you retire.
I'm 22, I've got myself a degree (in Computer Science with AI), have had 7 jobs (plus a paper-round). If you've got yourself some shitty degree in, like, Women's or Minority Studies from some middle/low tier Uni, and you've barely had a job except that one time you did a trial shift at Starbucks, but the manager was a bit of a dick, so you left 40 minutes in, don't expect to get $15 an hour. Hell, you'll probably find that to most employers, you're not even worth $7.25, and that's why you can't get a job, and why you now spend your life posting shit on reddit about how much capitalism sucks, and if only you were born in Sweden, life would be oh-so-grand.