Did Chase send a letter or some kind of confirmation correspondence confirming you being added as authorized user? Usually cards will just have the user's name on it, but we took photos of our cards and various account info showing that we are linked.
If I recall rightly, at the time I added my husband to my bank account, he did not yet have his SSN. They accepted his passport, marriage license, and other evidence.
Typically a K1 should try to obtain their SSN within two weeks of entering the US, and that opens up a lot of possibilities and ways of securing other items. If you've waited too late or you are adjusting from a different way (it sounds like you came a different way) then your next opportunity is going to be EAD if you're filing for that with AOS. That will also open up the ability to go back to the SSA and also to get state ID etc.
As far as other proofs goes.. health insurance, joint taxes, pension/insurance beneficiaries, life insurance, wills/POAs are all good. IIRC, we also had something like a Costco membership printed out where you could see him as a user on the account. We did the same with our phone plan.
In the future, once you've got your SSN, getting a credit card without credit history isn't as hard as one might think. Start with a secured credit card like through Discover, and within six months you'll be upgraded and should be good to go.