How can I childproof this 1957 cooktop?
You may not be able to find a timer that's designed to directly switch that much, but you can find a timer that switches a lot less, and use it to switch the coil of a relay that can switch whatever load you require. Relay coils take very little power to switch, and relay contacts can be had as large as you could possible need, or larger.

However, if you are not bound up in love with your 58 year old cooker, it may be a better idea to replace it; a relay capable of switching a typical cooktop load is not generally all that inexpensive itself, unless you can find one surplus.

A newER used cooktop is generally quite inexpensive - people remodel kitchens all the time and discard or sell off inexpensively perfectly good appliances that are not the right color, etc.