Although some gun dealers will have you wait from 3 to 7 days before handing the gun over to you that you're purchasing there's no Federal Law as of now that states the gun dealer has to wait that long or wait at all to deliver the gun to you.
It's usually up to local laws that the gun dealer and gun purchaser must follow when purchasing a gun.
In some places the gun dealer will be able to turn the gun over to you as soon as the background check is performed and you pay for the gun which can take a few minutes to complete.