It’s possible to do this in some states that only require a background check and an online test. But, you will be walking around with an out-of-state concealed carry permit. In Texas, if you are a Texas resident and have a Texas CC permit, you only have to fill out the form 4473 when you buy a gun. It never gets called into the fed for a background check. You just pay the man and walk out with the gun. That’s one of the perks of having a CC permit in Texas. But, an out-of-state CC permit won’t work for this.
If you live in Georgia you just pack it.