Two-time victor Garcia leads the way by four shots after posting a superb eight-under 64 at the Gary Player Country Club, registering eight birdies in his bogey-free round.
He also birdied the first two holes and ended with a tally of seven birdies, offset by bogeys on two of the four par-threes.
Lee was blemish free on Friday morning (NZT), and finished with two birdies.
It was the Spaniard's lowest opening round score of the season by two shots and matched the biggest first-round lead on the tour in 2018. He then found trees again and lost his ball.
Li Haotong and Lucas Bjerregaard also have outside chances at the Race to Dubai title but Haotong was six shots off the lead at the Nedbank Challenge and Bjerregaard was 10 behind.
A third player capable of ending the year as Europe's No 1, Lucas Bjerregaard, was 3-over.
Victory at Sun City would at least take the Northern Irishman to second on the money list and see him paired with Molinari for the opening round in Dubai, where players tee off in Race to Dubai order.
Garcia is seeking a third Nedbank title but first since 2003, while South Africa's Oosthuizen has never won his country's most prestigious tournament. He began with a birdie and twice reeled off three in a row.
"My thing is I'm coming here with the goal, if I can get into that final group on Thursday with Frankie next week, that would be a good start", McIlroy said, conscious that he's played in six final groups this year without success.
"After eight I had a good run at a few holes".
"I probably wasn't swinging unbelievably but I kept it under control and kept the ball in play all the time which is hard to do here".
"It's a tournament I've always wanted to play as a kid and I came here plenty of times with the family to watch".
The 38-year-old, who is going for a second consecutive win, having triumphed at the Andalucia Valderrama Masters last month, said in quotes on the European Tour website yesterday: "It felt great".