Would shaken Baby syndrome be a reason why babies head is so big?

No

Let me explain:

Shaken baby syndrome is a serious brain injury that can occur when a baby or young child is shaken violently. It can cause bleeding in the brain, swelling of the brain, and damage to the brain cells. Shaken baby syndrome can lead to lifelong disabilities, including mental retardation, cerebral palsy, blindness, and deafness. It can also be fatal.