There are several applications that allow to save a new credit card to a Google Pay. Upon pressing the button, the Google Pay opens with a credit card data pre-filled. However, I couldn't find any mentions of Intents or any API that allow to do that. How do I implement a "save credit/debit card to Google Pay" functionality inside an Android app?
I don't think what you are after is directly supported.
One question that I have for you is why do you want to save the card? Is it for the purpose of making a payment or for storing it for later use?
If the purpose is to make a payment, then I would suggest integrating with the Google Pay Android APIs which will give the user the option to either select from an existing set of payment methods or add and save a new payment method for immediate use.
If the purpose is to save a card for later use and you also happen to be a card issuer, then you can achieve this with push provisioning. See answer here.