How big did is this quilt going to be? Fleece is very smooshable so quilting it at the machine after you've got the top together shouldn't be much of a problem unless it's king size.
If you would rather, you can "birth" it with the fleece backing. If you were to smooth & baste it well without stretching it, birthing should work well. Put the top and fleece right sides together, smooth it all out & pin or spray baste it all together. Sew all around the edges except for about an 8" opening. Take out all the pins if you used pins, and turn it right side out. Just tack it, stitch in the ditch or handquilt it and you're finished. I like to sew around the outside edge again when it's turned right side out to make it "look" like binding.