Unless you had a contract for a certain period of time, you took the same risk as anyone else who quits a job for a bigger better deal. Even if you started working, you may have been terminated after a day or quit after a day.
While it is true that under Georgia law an employee can generally be terminated for any reason or for no reason at all, it sounds like you may have had a written contract (since you mention that you had an "offer letter"). The terms of a written contract might offer more protection than Georgia law. You should consult with a lawyer to determine whether or not there is anything you can do.
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