Seatbelts come around in the mid sixties. My 64 Galaxie had the "lifesaver" option which consisted of non retractable lap belts and a padded dash. Remember they were solid steel back in the day! Under a hundred bucks for that "option"
With a car like that going for a tumble, I'm not sure if a seatbelt would really be a good idea. Better to take your chances going for a little flight. Might land on something soft rather than have the car crush your head. They hadn't heard of roll cages either.