(CBS) The headlining figure in the White Sox’s rebuilding process surfaced at the big league level Wednesday night when top-rated prospect Yoan Moncada made his debut with the team, playing second base and going 0-for-2 with a walk.

So how quickly could other key young players of this rebuild follow to the big league level for the White Sox? Maybe late in the season, general manager Rick Hahn said in an interview with Brian Hanley and Barry Rozner on 670 The Score on Thursday morning.

“There’s a handful of guys, especially at the Triple-A level, who are starting to force the issue a little bit and showing that they’ve mastered most everything that you could hope they would at the Triple-A level,” Hahn said. “Similar to Yoan, it might be time for that next challenge that the big leagues present for a young player. So we’ve had conversations about who potentially could be next and whether it’s August or September, you know, it’s certainly conceivable we could see a couple more young faces up here.”

Though Hahn didn’t name names, right-hander Reynaldo Lopez is getting close to big league-ready. He has a 3.78 ERA with 101 strikeouts in 100 innings, and White Sox officials have previously praised his progress and development.

Right-hander Lucas Giolito and right-hander Carson Fulmer would be options as well, with both having previous MLB experience, but they’ve struggled to the tune of a 5.00 ERA and 5.42 ERA this season, respectively.

Hahn stressed that the White Sox won’t adjust a timeline for any prospect just because rosters expand in September.

“It’s more about the individual player than anything with regards to where the big league club is right now,” Hahn said. “It’s nice and it’s different from where perhaps we’ve been in recent years and that we have the luxury to just focus on what’s best for Player X’s development as opposed to, ‘Oh, we have a need here in Chicago, we need an arm tomorrow — who’s the best we can bring to help us win that game?'”

Listen to Hahn’s full interview below.