If the hood has a Lycra edge binding (the one in the O.P. looks like it might), it’s often possible to do a no-sew shockcord drawstring. The lycra binding is often tubular if only stitched on the edge. Forming a ready made channel for a cord.
I did this to the hem of my Uniqlo Ultralight down hoody.
Method:
Thread the end of some 2mm shockcord onto a darning needle, fold a few mm over and stitch together.
Decide where you want the cord to exit the hood edge, and wiggle the needle through the weave of the Lycra edging to its interior. Ease the needle around inside the hood rim to the other side (drawing the shockcord through behind) and then force the needle to exit at the opposite side to the start point.
Pull cord end out, remove needle.
Add mini cordlocks to each end and cut cord to length and Knot.
Done.