How to figure out the 4 digit code for expiration without having the physical card in hand
At least until some time ago, there was no link at all between the card number and the expiration date. I.e. I remember I got a new Amex card with the identical number and just a new expiration date shortly before the old one did expire. It may be different for other card brands and it may have changed.
Nevertheless, if the expiration date could be derived from the card number it would not make any sense at all as an extra security feature.