No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
I got approved for the green card few days after I froze my files. Granted the pre-approval was done using a SP before I froze my files.
They're still able to pull your credit for SPs to offer preapprovals.
With Amex, I have app’d, been approved for new cards, and received CLIs for existing cards with my file frozen.