You don't even need a new work box, or any box for that matter since coax is low voltage. Search the Depot for a Carlon 1-Gang Non-Metallic Low-Voltage Electrical Old Work Bracket SC100RR, approx $2.40.

Trace the size of the bracket opening around the hole that you have already made in the wall. Cut and square off the larger opening for the bracket with a drywall saw, utility knife, etc.

Place the bracket in the opening and tighten the two screws to get the clamping arms to swing out and secure the bracket to the wall from the backside.

Cover with a wall plate of your choosing. Blank, dedicated coax nipple, or keystone for future multimedia flexibility.