You are in an "at will" state, which means you can be fired at any time for about any reason, legally. Even though they hired you without a driver's license (you say, knowing you didn't have one, that's perhaps debatable, maybe no one thought to check?) they can, very legally, fire you at any time, and use as a reason that you do not have a driver's license which the company requires.
Your only recourse would be to file for unemployment insurance to tide you over briefly while you were looking for another job, and try to show that they knowingly hired you, without a driver's license, and then terminated you later, for something that was okay with them for a while, and then was used as an excuse to terminate.
They'll probably, of course, claim they didn't know, and then fired you when they did find out. So if you have any proof that they do know you don't have a license, keep up with it, write down the date and substance of any comments or conversations you have or have had that would show definitely that you have told them you don't have a license and/or the company is aware of it and yet have continued to let you work.
Meantime, I understand that sometimes costs are high, reasons why not are good, and getting a license or getting one reinstated is very difficult, but DON'T drive without one, please. The penalties for that would probably render you unemployed and unable to get future jobs, even if you have transportation to them.