I did this pretty much, except I did have a car and family, but I was stubborn and refused help from my family, so really just the car.

Get to a bigger midwest/ rust belt city (Indianapolis, Cincinnati, Pittsburgh, St Louis, Cleveland) cost of living is low which is good for you, and in my experience not many people are moving there so tons of people are hiring at jobs with no requirements (I got a job in like 2 days). Try and get two jobs close to each other, probably downtown. You'll save up money way quicker and have less time to deal with living on the streets.

Find a public park, preferably one with those grills and a water fountain. You can cook food over a fire on thee grill, simple things like oatmeal or ramen. The one I stayed in had bathrooms that were open during the day (at night I just did my business in the woods, used a bag for number 2). It also had an old public building that was closed down but I could climb on top and sleep under the eaves out of sight and the weather. I kept my stuff in my car but I could have kept it there.

For electricity charge you're stuff at work, and get a backup battery, they're only like 30 bucks and it's super important. Libraries are a godsend for a million things, electricity and bathrooms chief among them. After 3 months you should be able to save enough for a shitty apartment and have the job history. Lie if you need to, they won't check more than your current job 9/10 times.