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AFAIK there are no data points of people getting the CSP/CSR with that short a credit history. I don't think Chase considers AU cards while analyzing applications either, so it might not help as much as you think.
I would say you should wait till atleast 1 year before applying. In the meantime, you could apply for the Freedom or Freedom Unlimited cards. You will get a handy 150$ in UR for the sign up bonus, which you can transfer over to the Sapphire card once approved, and the history of payments with Chase will also probably boost your internal score with them. You might get better pre qual offers as well. Do you bank with Chase? That does also seem to help a bit in general.
I don't bank with Chase as I live in a state that they do not have a presence. However, the idea of getting a Freedom Unlimited card is a good one. I am probably going to do that and then apply again for the Chase CSR later. Thanks.
Check Chase pre-qual site, visit it every now and then. As soon as it shows the CSP apply for it.
I think that if you wait a few months the SL will be better.
Check Amex, Citi and Cap1 pre-qual sites. Check the cards/APR they offer. As you history improves the APR will be lower.
If you only have 1 card and 1 AU, I think you could get another card, maybe Amex or Discover while you wait for Chase. Amex should be 10K or more after 6-8 months, that will help you get good SL with Chase. Good luck.