It's up to the seller.  Some online sellers provide a certain number of days after package receipt to inspect the firearm.  If it's the wrong one, is not as described, was damaged in shipment, etc., they will work with you to replace it or issue a refund.  If you notify them after that inspection period, they may not accept returns.

The number of days usually ranges between 3 to 5 days -- enough time to make arrangements with your FFL to inspect it and provide notification if there's a problem.  This is especially important for handguns, since it'll be sitting at the gun store for weeks until you get a permit.  If it's damaged when you pick it up, you'll want to know if it arrived that way or if it happened during the 2 week wait for a permit. 

Depending on who's working and what day it was delivered, the employees may not immediately notify you it's ready for pickup/inspection.  If your tracking history says it was delivered, don't wait for a phone call.  Just go on down to the store.  Sometimes they get busy, people are out sick, or they might believe someone else already called you.  That's happened twice for my transfers.

You have the most to lose if the store doesn't notify you promptly.  Therefore, it's better to be proactive than to wait for a call after you know it's been delivered.