I just made a bag with foam, about 1/4" thick, in the middle. As I stitched, I pushed the foam down as it fed under the needle. I used a gadget that was originally created to aid with safety pins' closure. Wooden handle and metal 1 1/2" tip.
I also used the iron on interfacing that was very stiff. It made my fabric bubble, so, while it was hot, I flipped the piece over and pulled back the fabric, half side at a time, and re-ironed it smooth. (worked quickly)