"Just go out there and play and have fun," he said.
Davis said there are outsized expectations that come with being the top selection in the draft, and he can empathize with what Williamson is going through.
"I think he kind of feels it," Davis told ESPN on Wednesday while Williamson was making his NBA debut some 1,300 miles away. "I for sure felt it. I just feel like if you're the first pick, it's like you have to win Rookie of the Year. I didn't, Dame [Lillard] did, but there's some type of pressure where you feel like you have to.
"He doesn't now because he hasn't played in a lot of games, but you still want to go out there and perform. Obviously, the city of New Orleans has been waiting for him to play for a long time. So it's good that the city is behind him, the team is behind him. I'm pretty sure the players are also behind him. So it's going to be fun. It will be fun to watch him and kind of just see him grow."
Williamson scored 22 points in 18 minutes in his first game Wednesday, a 121-117 loss to the San Antonio Spurs. He shot 8-for-11 from the field (including 4-for-4 from 3) and added 7 rebounds, 3 assists and 5 turnovers.
If Williamson keeps up that type of production, the Rookie of the Year race could get interesting, but with Williamson having missed 44 games and Ja Morant lifting the Memphis Grizzlies to playoff contention with his play in the first half of the season, the award is most likely out of reach for the No. 1 pick.
Davis said he and Williamson, despite their parallel experiences coming into the league, don't have a relationship, but he would be open to one.
"He kind of hates me after he said I didn't give him an autograph in high school," Davis said with a laugh, finding the perceived slight a little silly. "I didn't really see him [at the time]. He said he wanted my autograph in high school or something like that.
"But no, I don't really have a relationship with him. If he ever wanted to reach out, I'd be more than happy to talk to him, just kind of walk him through my experience out there and just in the league in general."
With the New Orleans game still going on following the Lakers' 100-92 win over the New York Knicks, Davis, fresh off a 28-point performance, planned to rush out of the arena to find a spot to tune in to Williamson's game.
"I watched him a lot at Duke. I mean, he can jump out the gym. He's a freakish athlete. Some of the stuff he can do is insane. So I'm excited to see him play," Davis said. "If I make it to dinner on time and he's still playing, I'm going to watch the second half and just kind of see what happens. Just kind of tune in throughout his rookie year."
Sights and sounds from Zion's NBA debut
Look back at some of the best moments from Zion Williamson's 22-point debut for the Pelicans.