IIRC you can SBR any lower with the ATF. I believe that you will need to file a Form 1 and send $200 to the ATF and get your lower engraved with your name and city, state (or Trust Info). I also believe that you can use the lower for any >16" upper while you wait the 6+ months for your SBR stamp. You cannot have a barrel less than 16" in your house or you could possibly get busted for intent...
Yes, Form 1 is correct, waiting is the worst part of it, there are a few other things needed so do your research.
You can also by an SBR from a dealer as well but still have to wait.