The sensor does not detect the glass surface. Various hacks exist to get around this, of which the simplest is to place a thin metal layer between the bed and the sensor—see https://forum.snapmaker.com/t/for-all-who-want-level-on-glass/12437 for one solution (warning: very long thread). Other people have replaced the sensor with something that does detect glass, or simply level the bed manually.
People who have done glass bed mods here have used various types and thicknesses of glass. I don’t know of any reason why 3mm wouldn’t work.