Welcome to the Quilting Board!
I love the idea of the hammer.. and the puffiness in my middle says it just like to hang around..
Are you speaking of the puffyness from all the fabric being in that one spot from the seams meeting? A hammer should work I would put a piece of thick fabric over it to pound on it though or a rubber mallet. My daughters quilt is the same way.
[on the wrong side]:
1. At the center seam, cut the first stitch with scissors.
2. Remove the two or three vertical stitches at the center with stiletto or seam ripper.
3. Turn block over and repeat removing vertical stitches at center.
4. Open the center seams and push down flat to form a tiny four-patch.
This really works to flatten the seams in the back of the block.
I have no idea about the puffiness (the quilt or my waistline- lol) but I wanted to say how super cute your baby is in your avatar...