Full-time minimum wage workers cannot afford a one-bedroom rental in 95% of US

As a preface, I’m a white millennial who grew up in a southeast US middle class family. I’m completely aware my upbringing and experiences do not only not align with a large percentage of those in the US but probably even less than say 20% or so.

In saying that, I’ve always understood and expected minimum wage jobs to be one of a couple things:

1. A first job for young people who live with their parents, or at least aren’t depended on to pay the bills, who want to cut their teeth with what it looks like to have a job and/or have some extra spending money

2. A non bread winning family member looking to contribute a little towards day to day bills

Is there documentation or something from the government that outlines expectations for exactly what the minimum wage is supposed to accomplish for a person? Is it intended to be a “living wage” or arbitrarily set to something that folks in charge deem appropriate for some reason unbeknownst to me?

If it’s supposed to be a living wage it should be data driven based on cost of living and evaluated on a relatively high frequency (at least once per year). I know this is a hot political topic, but it just seems like another issue that we could use actual data to solve based on intent of what minimum wage should be instead of poking the right or left bears and polarizing the world more than it already is.

What percentage of the full time work-force in the US earns mimimum wage? And for how long do they earn this minimum wage before going on to earn more?