Most sellers have a limited amount of time for you to inspect the firearm you ordered. Most offer 3-5 days after delivery so you can make any claims for return.
So, even if you have to wait for your permit, DO NOT WAIT to go see your firearm at the FFL's place of business. Track the package and plan to go within day or two after arrival.
That way, if the seller messed up and sent the wrong firearm, or if it's damaged, or if it's just not as expected for any reason, you can contact the seller within the specified time limit.
If you wait until you get your permit to inspect the weapon, you might lose any right to a refund.