Well, you have been approved and have the card, so you might want to just go ahead and ask about the refi right away. Unless you have something extrodinary gonna happen to improve your credit short term, the worst case is that they say "no" which really will mean "not yet" since they did give you the card and you are now building a history and relationship with them.
I applied for a Navcheck LOC with NFCU on 4/29 they called to verify employement today and I was approved for the amount I requested. I also applied for a CC with them on the same date and have not had any response. I asked the rep why they pulled 2 diff credit reports when I applied the same day. The rep stated I applied at separate times and they will pull 1 cr if I call over the phone to apply for credit. I am now going to apply for a refinance auto loan once they approve my credit card request. I transfer money each payday into my checking/savings account with them on a bi-weekly basis.
I wasn't sure if I should try the CC 1st or the auto re-fi so I tried the CC. Shocked the heck out of me that I was approved. I've only had a savings account with them for a couple months. I've been putting money in there every pay day so far & in fact will be putting a significant amount in the end of the month so I was almost thinking I should have waited until then. I did ask about the auto re-fi & was told the same thing they had to pull another CR.
Seems kind of silly though since they already have my CR. I'm going to wait another couple months even though my current interest rate is killing me. This will give me a chance to charge a few things to the CC & pay it off so they can see I'm responsible about paying it & I'll have a few more payments on my auto showing up on my CR.
No what shocked me is that I got approved with a FICO of 566! Most folks have much better scores and/or higher incomes.