When buying a gun or a handgun there's usually no waiting period before you can purchase the gun.
No law or Federal Law exists that makes a gun shop or gun dealer wait to sell you the gun but they must perform a background check.
The background check in most places takes only a few minutes but some places may take up to 3 days for the background check to be completed.
Once the background check has been completed and you have no criminal history and are allowed to have a gun then you can pickup and purchase the gun.
As long as you're 21 years old or older some states don't even require a concealed or other weapons permit to carry the gun.