I would give it 3-6 months to generate a good score. that's how long it took me to generate a score after getting my first loan from my local cu. Since you are just starting out, ALWAYS ALWAYS ALWAYS PAY ON TIME! you'll be off to a good start
I would wait a few more months for your own cc to report. AU's are not gonna count on the fico 08 so I wouldn't even count on that for anything right now. I would ignore it. I'm an au on my husbands cc and its only reporting to one cra right now. I expect that to stop soon. I would wait a few more months though just to establish history. If you don't mind, how did you get the first cc and whos it through?