My bullshit theory is that the "God" of Sha'karee is a
Cytherian prisoner who was imprisoned for trying to take over the Cytherian "government". Before he was captured he retasked several of the Cytherian reverse exploration probes to send out telepathic signals that would convince a suitable telepath in range that their societies version of a deity was calling them to the center of the galaxy to find whatever their version of the Garden of Eden or paradise was.
Sybok heard this signal and began his crusade because of it.
Once he had captured the Enterprise, using his Cytherian enhanced mind he enhanced the Enterprise warp drive until it could achieve warp whatever speed and cross the distance to the Great Barrier in days, just like Barclay enhanced the Enterprise-D warp drive to reach the center of the galaxy in TNG The Nth Degree. The Bird of Prey cloaked and snuck inside their warp bubble so they could travel along.
The method of travel would blow up the warp drive if continued in use after the round trip to the center of the galaxy and back (to avoid it being used to return and attack the Cytherians) and since Sybok was dead none of the Enterprise crew knew how to reproduce it. And Barclay forgot how to do it as soon as he was "released" by the Cytherian mind probe anyway.
- Both the Cytherians and "God" present as giant disembodied glowing heads.
- Both the Cytherians and God use a person they've contacted and manipulated to bring a ship to them; the Cytherians to explore and meet other cultures without leaving home, and God to hijack a starship as a means of escape and/or conquest.
- Both involve enhancing ships to achieve vastly higher warp speeds.
- Both reside at the center of the galaxy.