The story was a thin paperback. Humans were dominated by some alien species but not limited to Earth when taken. Some sort of priesthood trained people for mental powers. Graduation was moving something like a moon or planet with your mind. The protagonist had to eventually move a sun. I read it in 1974 or so, so probably '60's. It did not have the feel of a '50's story.
You're looking for Conquest of Earth by Manly Banister, written in 1957. The Trisz are energy beings who rule the earth, stealing its water. Kor Danay is a member of the Institute of Manhood, a monk-like order which secretly trains its members in psychic abilities. The graduation consists of challenges. Kor is teleported to an unknown place in the the galaxy and has to quickly find his way back to Earth, then is required to draw the Fire Out of Heaven, bringing energy from the sun to a deserted planet.