I need to submit identity verification for my Apple Card

Unfortunately you need a photo ID (either drivers license or state ID) issued by a state. The ID from the state must show your current US residence, date of birth, and a photo. There are no exceptions to this for Apple Card.

How to apply for Apple Card - Apple Support

Several other banks do work with foreign students, most notably Bank of America, Capital One and Discover. All offer checking, savings and credit cards.

While I’m not privy to the exact criteria used by Goldman Sachs with respect to the ID number (Having an ITIN at least indicates a possible U.S. Federal Income Tax liability) …

… the point may be moot for you.

AppleCard is a credit card available to U.S. residents who are evaluated as a “good credit risk” thru data provided by U.S. Credit Reporting agencies.

I’m afraid that you’ll not even be “uncovered” in those checks; much less show a “history of responsible credit usage.”

How your Apple Card application is evaluated - Apple Support