I haven’t been playing too long, but racing is the best way (pretty much only) way to get cars. As you level up you are offered to by a new car at an extreme discount (400k credits). You can also get new cars sometimes in the Rivals section and sometime new free cars pop up. And of course, you can buy new cars when you have enough credits (which you get through racing).
While it will take you some time and effort to own ALL the cars remember you can rent cars as well if there’s one you want to drive but don’t actually “own” yet.
Don’t overlook the auction house. I’ve sold quite a lot of cars lately where I’ve ended up with duplicates, e.g. after I got the cars from last month’s bounty hunter rivals. I’m sure many other people will have done the same. I sold them for lower prices than the level up discounted price. At this stage in the game’s life there are probably more people like me looking to sell surplus cars than new players looking to buy them.