It didn't take long for him to make his way up -- he had tremendous natural talent.
Newman lived in Fairfield County, CT, a.k.a. "The Gold Coast." There was a Datsun dealer named Bob Sharpe (which was also the name of his dealership), also in Fairfield County. Bob Sharpe Racing use Limerock Racetrack in north western CT for practice, as well as racing SCCA and professional events at that track. Newman went to Bob Sharpe and bought a race car, and asked Sharpe to teach him how to drive.
HAH! In short order, Newman was beating Sharpe. IIRC, it wasn't long before Sharpe gave up driving and made Newman the team driver. He was THAT good. HE didn't race as "Paul Newman." Paul Newman was a movie star. He raced as "PJ Newman," and he tried very hard to keep the racing completely separate from the Hollywood hype. In the pits and on the track, he wasn't a movie star, he was just one of the guys.