As some professional miko are recruited through newspapers, classified ads or Hello Work (job-placement office), these may be practical means by which to land a job if you lack connections to people in shrines.
本職巫女の求人は、新聞・求人広告、ハローワーク等に掲載されることがあり、神社関係者で無い場合はそれらを探すのが本職巫女になる現実的な手段であろう。