No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
Congrats on your approval and welcome to the Chase Club!! In 12 months you can have the option to product change to the CSR, if you like! It's a much better card and totally worth it if you travel or dine out frequently.
I applied to a BoA card without SSN as well. But when I got it the card showed up in my credit file. It's attached to your name, DOB, and address as well as the SSN, so your history is as old as the first card you get.