Having an existing offer is a good idea, but I wouldn't totally write off dealer financing.

When you go through the dealer for financing, they get a portion of the interest that the bank takes out (finance commission). That lets them take the price of the car below what they paid for it, because they can still make a profit on the financing and trade-in.

Apart from that, there are sometimes pretty big rebates and rate incentives that OEMs offer when you take their financing.

I built a system that estimates what monthly payments a dealer can offer a customer based on what incentives they might qualify for. It's pretty common to see a difference of several hundred dollars a month between the best combinations and the worst ones (even with the same term).