Penguins can do something Thursday that seemed impossible six months ago — win the Stanley Cup

Six months ago the Penguins were a mess, a team in search of an identity and direction.

“We would get frustrated early on in the year. We would get scored on and the whole team would just tank and be done for the game,” defenseman Ian Cole said. “I think we really learned a lot of hard lessons in those times when we were floundering. We were, ‘We’re a great team. Everyone knows it, but how do we figure it out?’ ”

It took a coaching change and some significant roster changes to turn around a season that was circling the drain. In those dark days before and just after Mike Sullivan replaced Mike Johnston as their coach on Dec. 12, the Penguins could not have imagined being in the position they will occupy Thursday — the Stanley Cup will be in the house at Consol Energy Center and a victory over the San Jose Sharks in Game 5 is all that stands between the Penguins and the franchise’s fourth Cup championship.

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It would be the first major Pittsburgh sports title to be won at home since the Pirates beat the New York Yankees in the 1960 World Series.

“If you asked us then would we be here, a lot of guys would have been like, ‘No,’ ” Cole said Wednesday after the Penguins practiced in suburban Cranberry Township. “A lot of guys still had faith we would make the playoffs when we were out of the playoff picture. … We had to go through some hard times to figure out how to do it, and I think we’re better for it.”

It didn’t happen right away. They lost their first four games after Sullivan took over but his commanding presence and persuasive voice, reinforced by infusions of speed through trades and call-ups from their farm team, transformed the Penguins into a powerful force.

“It seems like it was a long ways away. It seems like an entirely different season,” veteran center Matt Cullen said of the slow start.

They were 33-16-5 under Sullivan, including wins in 14 of their last 16 regular-season games. Their speed and cohesive defensive play have been great assets in the playoffs.

“We’re not going to come out and outpound teams like Washington and like San Jose. We want to force our game upon them,” defenseman Ben Lovejoy said.

They’ve succeeded. The Sharks have been flummoxed by how quickly the Penguins’ defensemen get the puck up to the forwards and rush up ice. In addition, the Sharks’ offense has been stifled by the Penguins’ relentless defense. San Jose center Joe Pavelski had no points in the first four games of the Cup Final after recording 22 points, including a league-leading 13 goals, in the first three rounds. Defenseman Brent Burns, an offensive catalyst, had two assists in Game 1 but hasn’t been heard from since.

And there’s the inescapable fact that the Sharks haven’t played with the lead in the Final. Their only victory in the first four games came in overtime, a 3-2 decision in Game 3.

Playoff leads have been a problem for the Sharks, who squandered a 3-0 series lead over the Kings in the first round in 2014. Coach Peter DeBoer, who wasn’t the Sharks’ coach then, tried to somehow spin that into a positive for his players.

“They’ve been on the other side, up 3-0, saw how quickly that vanished against L.A.,” he said. “We have some guys that vividly remember that. They know how quickly a win can turn the momentum.”

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Getting a lead would help them get that elusive win. Chasing the Penguins every game has forced DeBoer to disrupt his four-line rotation and put everyone out of rhythm. The Penguins, of course, hope for a repeat performance Thursday.

“We are completely focused on coming out and playing the exact same way we’ve been playing for the last four months,” Lovejoy said. “We want to come out and have a great start. We’re playing a really good team. We don’t want to give them any life.”

The Sharks were lighthearted and loose Wednesday, which DeBoer was happy to see. “I would have been worried had they come in quiet or dragging a little bit,” he said. “It was business as usual.”

It was business as usual for the Penguins, too, which for them meant a full, focused practice. “We worked on things out there today that we think will help us in the next game,” Sullivan said. “That’s been our approach all year, that we’re trying to get better every day when we come to the rink.

“I don’t think you ever arrive. We can always get better and improve. I think it’s that insatiable appetite to improve and get better that has allowed this team to get to the point where it’s at. We’re going to keep pushing until we achieve our ultimate goal.”

That goal, so unlikely six months ago, will be within reach Thursday.

Helene.Elliott@latimes.com

Twitter: @helenenothelen

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