I have been a Star Trek fan for many years but I'm not much of a scientist. I learned something not so long ago about Star Trek that literally blew my mind. Everything you see in Star Trek, every series, movie, etc. takes only place in our galaxy. The four quadrants (alpha, delta, gamma, etc.) refer to a quadrant of our galaxy, not the universe. Apparently there are billions of galaxies out there...
and actually mostly all eps/movies take place in the alpha quadrant except voyager and a bit of ds9.