The only viable options for the hobbyist is a network using unlicensed bands (like 2.4 GHz / 5GHz, or the 33cm ISM band) along with CBRS[0]. As I understand it, most UEs (handsets) that support one of those bands will not use it exclusively—only in tandem with another licensed band.
The other alternative is Amateur Radio bands, which some hams have apparently experimented with: https://github.com/mmtorni/HamLTE.
[0] https://en.wikipedia.org/wiki/Citizens_Broadband_Radio_Servi...