Will my new iPhone 14 max pro work in Costa Rica ?

It works if you have eSIM providers in your country among this list:--> Find wireless carriers and worldwide service providers that offer eSIM service - Apple Support , since iPhones 14 manufactured for US market DO NOT use phisycal SIM cards.

(sorry, I don't see any eSIM carrier in Costa Rica).

Regards

Giulio

Contact a cellular carrier in Costa Rica, explain your needs, and see if one of them can help you.

Regards

Giulio