I had a similar experience last year (car was paid for in cash, but, I was on the title, not my son). First, the loan and title are two separate issues.
About the title. You will have to do a little reading on how car sales work in your State. In mine (TX), and probably all, there is a sales contract for a car. Whoever signs the sales contract goes on the title. The contract may also give details about how titling is going to proceed, but there's going to be State laws governing this process. So get a copy of the sales contract ASAP an look it over.
In my State, I didn't even have to contact a lawyer, because there is an enforcement agency to report non-compliant car dealerships. I'm sure your State has one too. You'll want to look at the State where the dealership resides. They probably have a portal to submit a complaint online. It'll be a pretty open-and-shut case if you're not on the sales contract and they put you on the title.
As for the loan, no personal experience here, but again get a copy of the loan docs and report the violation to a State enforcement agency. I think it's another easy case for them.
My feeling is employees at car dealerships are instructed to do illegal things like this, and they get away with it most of the time because people don't know what to do. Lawyers are expensive and there isn't a lot of $ damages so that route isn't worth it. But the State agencies are really good at cracking down and fining dealerships as the case may be. My case was resolved in a few weeks, and boy did the car dealership change their tune after the State went in there!