If I was making it, I would cut the bottom piece with a seam down the center, adding seam allowances. Stitch the bottom pieces together leaving a turning gap in the center. Then sew the bottom to the hat, right sides together, by machine. Turn right side out, stuff, and ladder stitch the opening closed. The seam won't show and you would just have a small gap to sew closed rather than sewing on the entire piece by hand. Clear as mud??