Have you tried the Amex Prequalified Offers ?
Depending on how long ago you opened your first Amex card. You might be able to check for offers in private browsing by going to the website and check for offers.
If it asks you to login. Login and then go to personal card offers. Find PRG. And hit apply. It will tell you at the top of the next page if you are Preapproved.
Normally Amex denials are SP once you have 30 days of card membership and your FICO score has updated on the website. A rep told me that.