Oliver made his debut in a one-race deal in 1971, racing at College Station, starting 19th in the race. An engine failure would sideline Oliver to 32nd place for a rather dismal debut.
Oliver moved to Donlavey Racing in 1972, competing with that team for seven events on the year. In his debut with the team at Rockingham, Oliver earned his first career top-10 start with a tenth place start. However, he finished that event 40th and continued to struggle finishing races. In seven races, he only finished one race. However, it was worth it as Oliver finished 4th at South Boston, his best career finish. On the flipside, Oliver's best finish other than the Dover race was a 22nd at Darlington and Oliver lost his ride.