Chris, unless your firearm has a "pick your serial number" choice, the serial number is not listed on your order. You don't actually own the firearm until your receiving FFL transfers the firearm to you. This is the reason no serial number is listed under normal circumstances. Cheers and stay safe!

Chris, You won't see your serial number of the firearm until your FFL receives it to transfer to you.

They don't put the serial number in you order history. And if the order hasn't been pulled from inventory yet there wouldn't yet be a serial number to give you.
If you have a "item has shipped" notification and you want or need a serial number, you'd need to contact customer service and they could look that up for you.
Call buds during buissnes hours at 859-368-0371, 9am-9pm eastern Mon-Fri
use the Blue Chat now button at the bottom right corner 9am to 9pm Mon - Sat and 9am to 7pm Sunday