How to relocate states with no car

I’m in Arkansas. I’ve lived here for at least 12 years and I’ve only been out of state once. I had moved to Michigan with my then partner and was there for a year. I had to come back bc we broke up so I’ve been back for a few months. I now yearn to move out of the south. I’m trans and I obviously don’t do well in a red state and so when I moved to Michigan (blue state) I was in love.
PROBLEM!
I live in a small city where jobs are very limited so I have to work for $11 an hour. I do not make much and I do not have a license or car. I’ve been having issues with my proof of residency and my ID being out of state and whatnot. But I have $2k saved up which I planned to get a car with. I’m really thinking about moving to Chicago bc of the walkable lifestyle and not needing a car to get around. My bus ticket would only be $200 from my city to Chicago. So if I move to Chicago with no car then I wouldn’t need a car to get around bc it’s walkable but if I get a car and then move I most likely wouldn’t need it. So.. should I wait to get my car and license or attempt to go to Chicago via bus?

I also do not have a lot of belongings either. I’d find roommate to stay with so I have a place to stay. I’m just tired of living in the south and want to live in a big, walkable city and I get it is expensive but I’m willing to put in the work.