That's so adorable!
Yes, removing some of the edging around the face will open it up and even eliminating the fold. Take out the edging rows until there's only about 1-1.5" and then binding off will opleave more room. On the next one, you might also knit flat for several more rows before rejoining to knit in the round. That will lengthen the opening as well.
Still, this looks so cute and cozy on your son.