First, there was his best buddy, Matthew Tkachuk, selected sixth overall by the Calgary Flames.
Then, the very next pick, another good friend, Clayton Keller, scooped up by the Arizona Coyotes.
A few more minutes passed, and Logan Brown was picked 11th overall by the Ottawa Senators.
Four picks after that came the moment Kunin had been waiting for his entire life: He had been selected into the NHL. When the Wild chose him with the 15th overall pick, Kunin became the fourth alumnus of the St. Louis Blues AAA team to be selected in the first round of the 2016 Draft.
"At the time, you didn't even realize how cool it was," Kunin said. "But to all play together, and all get drafted high like that and to be able to share it with them, it was pretty cool. It's something we'll remember for a long time."
Kunin credited Tkachuk's dad, longtime NHL forward Keith Tkachuk, and former Blues Jeff Brown and Jaime Rivers, among others, who helped launch the first generation of St. Louis hockey players.
It was their commitment to the AAA program there, along with their presence and willingness to coach, that helped the first "generation" of NHL stars from the area, including current St. Louis Blue Paul Stastny, Edmonton Oilers forward Patrick Maroon and Dallas Stars netminder Ben Bishop.
The Luke Kunins, Matthew Tkachucks and Clayton Kellers of the world are just the latest to be selected from the area dubbed the "Heartland of Hockey," and there are plenty more on the way.
"They were taking the time out of their days to teach us and make us better players," Kunin said. "That's really where it all started was with those guys."
Kunin entered the draft with an impressive resume.
He had been a captain at virtually every level he had ever played. He had starred for the United States at several international events, including a second-place finish at the Under-18 Five Nations Tournament in the Czech Republic.
He captained the U.S. Men's National Under-18 team to a gold medal at the 2015 IIHF Under-18 Men's World Championships.
He was coming off a spectacular freshman season at the University of Wisconsin, in which he registered 19 goals and 32 points.
Kunin was also believed by many to be the top two-way player in his draft class. He later went on to captain Team USA to a gold medal at the IIHF World Junior Championships, beating the Canadians on Canadian ice, while also becoming the first sophomore captain at UW in four decades.
"I've gotta keep reminding myself, he's 19 years old," Wisconsin head coach Tony Granato told Wild.com last winter. "I just think he represents everything you want in a player, in a leader and as someone who is a part of your program. He cares, he's a competitor, he's not afraid to say what's on his mind. He stands up for his teammates."
Granato was the right man at the right time for Kunin, who began his career with the Badgers playing for former North Star Mike Eaves. In a bit of irony, it was Eaves who was the last sophomore captain at Wisconsin prior to Kunin, wearing the 'C' for UW in 1975-76.
Eaves wasn't around for Kunin's sophomore season, but Granato, a long-time NHL player and a former Badger player, made a tremendous impact on his career.
Kunin was selected in the first round of the draft three months after Granato was named coach, so there wasn't any doubt about what the player's future was.
Instead of blowing smoke, Granato was realistic about Kunin's future at Wisconsin. Also a former head coach in the NHL, Granato took Kunin under his wing for the one year he had him and prepared him for life in the NHL.
"There's a long list of things he's taught me," Kunin said. "I can't really explain how important he was to me, and still is. And of all the things he's taught me, he's an unbelievable teacher, man, coach, you name it."
While Kunin has always taken pride in being a two-way player, it was under Granato's tutelage that that area of his game really took off.
"Just the details; always working, doing the little things, those were things he helped me with," Kunin said. "It was huge to have him. He knows what it takes to get here (the NHL) and he knew I was hoping to be there soon. It was an awesome fit for me and I'm just so thankful I got to learn from him for a year."
Nobody was more disappointed in not making the Opening Night NHL roster than Kunin, who had made it one of his goals way back when the summer began.
It was a process for him; first, he wanted to have a great Development Camp in July. He wanted to use that as a springboard into the Traverse City Prospects Tournament in September, and use that as fuel for a strong training camp back in St. Paul.
After the Wild signed veteran centerman Matt Cullen, Kunin's path to Opening Night seemed a bit more clogged. It didn't deter him from his goal, however.
"I think it should be anyone's goal that signs pro, to try and make the team and play in the NHL," Kunin said in early September. "For me, it's getting better every day, learning every day and at the end of the day, [Minnesota] is where I want to be so that's where I'm going to work to get."
Despite a strong showing in Traverse City and a training camp where he was among the last players cut from the roster, Kunin began the regular season where he ended last year, with Iowa in the American Hockey League.
But as he does -- and as he has at other levels -- Kunin took the news like a pro, vowing to work on his game and be ready when Minnesota called.
That's because if you didn't know he was 19 years old, you'd never guess it.
"He's a very serious young man," Wild coach Bruce Boudreau said earlier this fall. "He's going to be a real good hockey player for many years."
Little could he have known that his stay in the AHL would be so short.
Minnesota sustained three injuries in a game at Chicago on Oct. 12, which opened the door for Kunin -- thanks in large part to the big impression he left on coaches and staff all summer and through camp -- to make his NHL debut in Game 4, Minnesota's home opener against Columbus.
Because the Wild was without Mikael Granlund and Nino Niederreiter for several games, and remains without Zach Parise and Charlie Coyle, Kunin has gotten an extended look with the Minnesota roster, one where he has slowly but surely, gained the trust and admiration of his coaches and teammates.
Early on, Kunin was playing on the third and fourth lines centered by Matt Cullen, who made his NHL debut a few weeks before Kunin was born in 1997.
By his first road trip, one week after making his debut, Kunin was killing penalties late while protecting a one-goal lead. Soon, he moved from a bottom-six role into the top-six, skating on a line with Eric Staal.
Last week, Kunin even saw time on the power play; all of this despite the returns of both Granlund and Niederreiter to the lineup.
"It's his drive and his work ethic and his willingness to soak things in and to learn," said Staal, who had the primary assist on Kunin's first NHL goal on Oct. 26. "You have to do that at a young age, but he's eager to get better every single day, and I think he's done that. Every single game, I think he's improved."
Staal would know a thing or two about playing at this level as a teenager. He debuted with the Carolina Hurricanes as an 18-year-old in 2003, a few months after being selected with the second overall pick. Three weeks after debuting, Staal celebrated his 19th birthday.
Kunin turns 20 on Dec. 4.
In a dressing room full of players who have worn letters in their career, including Staal, Matt Cullen, Ryan Suter, and current Wild captain Mikko Koivu, Kunin is trying to absorb as much as he can.
"Just seeing the way they handle themselves and seeing the details, how hard they work in practice; those are the reasons why they're the best players," Kunin said. "Mikko is always the hardest worker in practice and in games. There's a reason for that, and that's what I'm trying to learn and soak in as much information from them as I can."
One of those players with a natural sense of leadership, Kunin has chosen to tread lightly in a veteran locker room. He said he wants his style of play to do the talking, and so far, he's had no issues doing anything asked of him, including going to the hard areas in front of the net.
That's even meant venturing near the blue paint and mixing it up with older, established veterans like Dustin Byfuglien of the Winnipeg Jets.
Kunin's older teammates have taken notice.
"You can sense he's a leader," Staal said. "He's gonna play in this League a long time and it's fun to be alongside him at the early stages of his career. He's learning every day. He's going to be an important part of this organization for a while."