I was reading about thermal and non-thermal radiation and I was wondering if visible light can be emitted from a non-thermal source?
Yes, LED's, luminescence of phosphorous (CRT screens), most of the current screen technology, fluorescent lights. They aren't a thermal source. They heat up due to the electric current but that's not the working principle.
Super-continuum sources are well known non-thermal white light sources. The gist is a laser beam interacts with a specially tailored nonlinear material to generate ultra-broadband coherent light. A few references: