I’d recommend using your rewards card a lot, but not using it to pay off the car.
Car loans or any installment loans are merely a tradeline on your credit score and thus paying off the car loan early really doesn’t mean much one way or the other. If the interest rate is high and you have cash pay it off, because a car loan is neither helping nor hurting you.
On the other hand if you use the credit cards sparingly such that small balances do show up on your credit report (cycle different from paying it off) that will help improve your score.
One of the factors that helps is outstanding credit available. Another is that you keep balances to less than 10% of the total credit available. If 10% is too hard, 30% is much better than say 50%.
You have a lot of time. If you want to get into the 800’s you need to use credit cards at some point, you just don’t need to carry a balance.