Every sewing machine has a zipper foot (sometimes called the Zip Foot). Either the foot stays in place and the needle is moved or the foot can snap to one side or the other of the presser foot arm.
I like to use a zipper foot with an adjustable guide. Normally, when you use the zipper foot to sew a zipper, you use the guide at the edge of the fabric.
But, you can feel where the zipper teeth are and use that to guide where your seam is sewn! I find the “finger” on the end of the adjustable guide will glide right along the zipper teeth to keep your seam in the right place.