I think you will get it. When you first got your credit card, your credit score was likely just as low as someone with bad credit because you haven't established anything yet. 749 takes into account the length of your credit history. Combine with the fact that car loans are often easy to get because there is collateral, and you are providing $5,000 down payment which really helps. You may have a limit as to what you can borrow because of your income.
On the other hand, at your age, I would consider a reliable preowned vehicle. I bought a 91 Corolla when I was 19 for $4,500, 11 years old with 229,000km at the time. Finally sold it when I was 25 with 365,000km on it for $800. I only put $2,000 into major maintenance/repairs for it during that time: Timing belt, water pump, clutch, alternator, and battery. So excluding minor maintenance, fuel, and insurance, the car cost me $1,000 a year to drive.