designing a mains powered car jump starter
200A * 12V = 2400W
So it would be in the realm of possibility from a 240V 16A socket. However a starter can require much more surge current than that, so if all you have is a 240V 16A socket, and a 12V 3600W DC supply, that would make a rather wimpy car starter.
This is never done in practice because it makes no sense to buy an expensive, high power DC power supply and use it for five seconds every year, at most... and it won't deliver enough power anyway.
Also it would be more expensive than a battery.
It makes a lot more sense to use a battery charger to charge the car battery, then use that to start the car.
Pretty much the only practical solution cost-wise is to put a super high current LiPo battery in the device along with charge &amp; management electronics, although that does introduce other spectacular failure modes... But it also makes it portable, which is useful if the car you want to start is not in your garage.