The back of my first quilts look just the same. Didn't know about walking feet, or indeed about much at that time. Quilts are still in use, and still loved. Your next one will be better.

On your next quilt make sure you smooth out the backing. I use clamps from Home Depot. I clip them to my glass top dining room table. I use large safety pins to hold the three layers together. Congrats on the new baby girl.

Welcome to this board.

I agree. I can take in an inch with spray starch and a steam iron - a method recommended by Kelly Cline of Vintage Quilting.

I have a friend who is a prolific hand appliqué stitcher. Her Moto is “when in doubt cover it up. Love the heart idea above in a real tiny print. My friend fuses the appliqué on, then hand stitches around it with single embroidery thread and very close stitches in a buttonhole stitch. It would look very intentional and no one will ever know. If you don’t hate doing the appliqué scatter a number in different sizes over the backing. The time you put into doing that will make the quilt even more special.

this sounds like a better idea than unsewing!

This is your first quilt for your baby. Don’t try to fix it. Just wash it and enjoy it. Your baby will love this quilt when she is older and be proud of it. (Washing will shrink the fabric a bit and you will not notice the puckering as much).

Your next quilt will be better by what advise everyone here is giving you.