Hi Perry,
yes,I have used Priority Insured USPS (both before I was licensed and after) and had no issues. Both hubs for the common carriers are not close to my location.
Here is the ATF link-note they recommend Registered-which takes a lot longer as every person who touch"s it has to sign for it ;
https://www.atf.gov/content/firearms-frequently-asked-questions-unlicensed-persons"Q: May a nonlicensee ship a firearm through the U.S. Postal Service?
A nonlicensee may not transfer a firearm to a non-licensed resident of another State.
A nonlicensee may mail a shotgun or rifle to a resident of his or her own State or to a licensee in any State. The Postal Service recommends that long guns be sent by registered mail and that no marking of any kind which would indicate the nature of the contents be placed on the outside of any parcel containing firearms. Handguns are not mailable. A common or contract carrier must be used to ship a handgun.
[18 U.S.C. 1715, 922(a)(3), 922(a)(5) and 922 (a)(2)(A)]