USB-C as a high current power source
With USB Type C the power can be up to 3A @ 5V without any negotiation.
To go beyond that (up to 5A @ 20V) requires negotiation over the CC lines.
There are USB type C connectors that work with a 0.062 board such as Wurth 632723300011.

Here is a good article on USB Power I found:

https://www.digikey.com/en/articles/techzone/2017/mar/designing-in-usb-type-c-and-using-power-delivery-for-rapid-charging