If you have a credit union, go through them first. Dealer financing is typically a second plan unless you had a report which looks like mine did when I needed a car.
Beyond that you likely know your credit score if you were credit card chasing, can you provide that? Also do you have any auto loan on your record in the past? Auto loans are the easiest loan type to obtain, so while sure it was suboptimal getting credit cards right now it's hardly the end of the world and even an unpretty dealer loan can be refinanced in a year easy in your situation, and probably after the six payment reports on the loan, by which time all your credit cards will be more than six months old too.
I did a similar two-step with my used card with a bunch of new accounts opened up after financing the vehicle, so really six months is fine though mine turned out to be 8 months so I could easily verify income from my new job.
