My German Shepherd got a CSP at about eight. My Australian Shepherd got the United card at about nine. Of course that is 56 and 63 for them.
Chase doesn't ask for SSN so I don't know how to pull their credit reports, but they do have credit profiles since I can pull up pre approved offers for them with the card match tool. They get mailed offers on occasion too. Your might be able to call to add the SSN. I know I had an AU card of my parents at 16.