So hee's what I know... o. Federal law prohibits anyone with a felony conviction from possessing a firearm or ammunition. It doesn't matter whether it is your first, second, third or fifth felony. The prohibition applies to all felony convictions, state or federal.
In Georgia, where you are from, the law specifically prohibits felony first offenders from receiving, possession or transporting a firearm. If the felony you are on probation for is a non-forcible one, the penalty is not less than one nor more than five years. If you are on probation for a forcible felony, a conviction of receiving, possessing, or transporting a firearm carries a mandatory five year sentence. If you are convicted of attempting to purchase or obtain the transfer of a firearm while on probation for a felony first offense, the penalty is at least one year but not more than five years.
There is an exception if you have been pardoned for the felony by the President of the United States, the State Board of Pardons and Paroles, or the person or agency empowered to grant pardons under a state constitution and, by the terms of the pardon, have expressly been authorized to receive, possess, or transport a firearm.
Another exemption applies to those who are granted relief by the secretary of the United States Department of the Treasury.
In short, only if you get the felony expunged or receive a pardon will you be able to legally possess a firearm.
Perhaps your felony was a deferred adjudication or deferred judgment. In that event, after a period, provided you don't violate the terms of your probation, the felony is dismissed. Once it is dismissed, you would be able to possess a firearm, since you would not be considered a convicted felon.
I suggest you obtain a copy of your conviction papers to determine if your felony was subsequently discharged without court adjudication of guilt. If it wasn't, and represents a permanent conviction, your only options are a pardon from the President of the United States or having your felony conviction expunged. To obtain an expungement, I recommend you retain counsel in Georgia who can advise you as to the likelihood of success and, if it seems feasible, prepare the proper paperwork for you.