With their four top players all 22 or younger - including NHL scoring leader Sidney Crosby, who is all of 19 - the Penguins anticipated going through a transition season before developing into one of the league's better teams.
Right now, that learning curve looks more like a straightaway.
After beating Trotz's NHL-leading Predators 4-1 on Tuesday, the Penguins are 9-2-0 in their last 11 games and are closing in on the top four in the Eastern Conference. Unless there's an unanticipated breakdown in their final 29 games, the Penguins are well on their way to making the playoffs for the first time since Mario Lemieux's comeback season in 2001.
"I'd hate to play them two years from now," Trotz said. "They're building something very special in Pittsburgh, and the city should be pretty excited."
No doubt their fans would be more revved up if that building plan included a new arena - the team and Pennsylvania state are negotiating how to pay for a replacement for 45-year-old Mellon Arena, but an agreement has not yet been reached.
But the Penguins' improvement has been so rapid, and young stars such as Crosby, Evgeni Malkin and Marc-Andre Fleury are playing so consistently well, it's easy to overlook their shabby surroundings.
With a 27-9-17 record and 63 points, the Penguins have surpassed the 58 points they had during a fourth consecutive Atlantic Division last-place finish last season. They had no more than 69 points in any of those four seasons.
"We're happy with the way we're playing," Crosby said. "We're doing a great job of competing right now."
With four players drafted No. 2 or higher since 2003, the Penguins are long since removed from those days a few years back when they were dumping players such as Jaromir Jagr, Martin Straka and Alex Kovalev for financial reasons.
Crosby, arguably the league's best player, has 86 points in 50 games and is on pace to have the most points of any NHL scoring leader since Lemieux's 161 in 1996. Joe Thornton's 125 points last season are the most since then.
Just as Jagr complemented Lemieux in the prime of his career, Crosby has plenty of help.
Malkin, the No. 2 pick in 2004 behind Washington's Alexander Ovechkin, has a team-high 26 goals going into Thursday's game at Philadelphia. Jordan Staal, the 18-year-old brother of Carolina star Eric Staal and the No. 2 pick last year, is one goal away from 20 - and he wasn't even expected to make the team when training camp began.
"It's amazing what he's doing," teammate Mark Recchi said. "I think he's gone beyond all expectations."
The biggest difference in this team from the Penguins who had won only 12 games at this time a year ago is the 22-year-old Fleury, the No. 1 draft pick in 2003.
More mature, confident and in control, he has been the Penguins' best player during their current hot streak and is on the verge of becoming one of the league's top goalies. His 2.74 goals-against average is down half a goal a game from last season, and he has all but two of Pittsburgh's 27 wins.
"He's been the difference in so many games," Crosby said of Fleury, who is 11-3-1 in his last 15 starts.
Helping bring all of this youth together is the 39-year-old Recchi, who starred for the Penguins' first Stanley Cup-winning team in 1991 before later playing for the Montreal Canadiens and Philadelphia Flyers. He re-signed with the Penguins this season after being dealt by Pittsburgh to eventual Stanley Cup champion Carolina late last season.
To Recchi, these Penguins lack only the overall depth of those Hurricanes - and new general manager Ray Shero could address that by the Feb. 27 trading deadline.
"The guys are learning how to win in this league, doing the right things," said Recchi, who recently had 10 points in three games. "We're starting to know what it takes to win. The effort is there, and now we're doing smart things every night. We're getting the puck deep when we have to, we're winning battles.
"If you continue to do that, and use the speed and skill we have, we're going to be tough to play against," he said.
Coach Michel Therrien's structured system was played by many of the current Penguins at Wilkes-Barre/Scranton of the minor AHL, where the one-time Montreal Canadiens coach was working until replacing Eddie Olczyk in Pittsburgh 14 months ago.
As Therrien constantly rolls four lines, the system relies on controlling the puck as much as possible, playing intelligently at both ends of the ice, taking plenty of shots on the power play and always being properly positioned in the defensive end.
"Everybody has bought into it, what we're trying to do, and everybody feels good in their roles," Recchi said. "Everybody is getting minutes, and everybody feels part of it. We're growing as a team right now."
The Predators aren't the only team wondering what the Penguins might become very soon.
"You knew that, with all that talent, it was just a matter of time," Washington's Chris Clark said.