May a private citizen register a firearm not previously registered in the National Firearms Registration and Transfer Record?
No. The NFA permits only manufacturers, makers, importers, and certain governmental entities to register firearms.
[26 U.S.C. 5841(b) and 5861(d); 27 CFR 479.101(b) and 479.104]
Source ATF: https://www.atf.gov/firearms/qa/may-private-citizen-register-firearm-not-previously-registered-national-firearms