Time was tight. Puck drop for Game 3 of the opening-round playoff series against the Hawks was 1:00 PM, an hour and a half away.
"Funny thing is, he wanted to introduce himself to everybody,'' recalls Coates. "So he's going around the room, shaking hands with every player.
"And Theo Fleury gave him a look and said: 'Uh, this is great but you might want to sit down and get your gear on.'"
The Calgary Flames lost that afternoon, 7-5. Iginla wore No. 24, sported a box-square helmet and played centre - yes, centre - on the top line alongside Fleury and German Titov, chipping in with an assist.
Two nights later, he'd officially open his big-league account, notching his first NHL goal at 5:53 of the second period against Eddie Belfour, even though the Flames were swept out of the playoffs in the minimum number of games.
A series might have been lost over those 48 hours and although no one could've possibly realized it at the time, something else, something immeasurable, had been added.
Two decades have passed since. The Jarome Iginla we see now, arriving with the Colorado Avalanche for Wednesday's 'Dome date, long ago made the succeeding transitions from raw-boned teenager to emerging pro to finished product to slam-dunk Hall of Famer.
A franchise icon in Calgary. The organization's all-time leading scorer. One of only 16 men in history to suit up for 1,500 regular-season games.
Back in the spring of '96, though, he was nothing more or less than an elite prospect traded for the current star of the times, Joe Niewuendyk, with a big, blue, limitless horizon stretching in front of him and plenty to prove.
Think of that time frame as a wonderful first pencil sketch for what would become a masterwork in oil.
"Could I tell right away?'' grunts Fleury. "Well, there aren't many kids who go from playing junior to getting on a plane and showing up for a playoff game against the Chicago Blackhawks the next day, right?
"So did I think he was going to be special?
"I told him once, early on, I thought he could be the best player in the league. I was serious. I don't think he believed me.
"We knew he'd be a good player. Kamloops was a factory then for turning out good players.
"He was a shot in the arm for everyone."
The details of the final stages of negotiation involved Coates sitting in his office at the Saddledome late on Dec. 19, 1996, the NHL trade embargo fast approaching.
"Through the whole process,'' Coates recalled years later, "my message had been, 'If you're acquiring Joe Nieuwendyk from us, the guy we're getting back is someone we're going to watch play for the Calgary Flames at a very high-level for the next 15 years.' Simple as that."
Of 13 original suitors, by that night nearing the Yuletide break only two remained.
"Ten minutes before the freeze,'' continued Coates, "I've got the New York Rangers on one phone, the NHL on one phone and Dallas on a third phone.
"New York opted out - pulled the young component from the package they were offering. But I was determined to get something done. No waiting until after Christmas.
"Dallas had been persistent. And (Stars' general manager) Bob Gainey had been pure, pure class throughout the whole thing.
"And so I made the deal."
Someone named Jarome Iginla, whom Al Coates had as yet never seen play live, the 11th overall pick in the 1995 NHL Draft, was officially a Calgary Flame.
Another of the organization's youthful corps of attackers of that era, centre Cory Stillman, was beginning his second NHL campaign when Iginla climbed aboard.
"In those first two (playoff) games,'' says Stillman, now director of forward development for the Carolina Hurricanes, "he instantly became a fan favourite. Joe Nieuwendyk, as everyone knows, was a great player. A Hall of Famer, like Jarome will be some day. Joe had everything. Was captain of the team. Had won a Stanley Cup. 50-goal guy. So well respected.
"But it didn't take Jarome long to win the city over. Just two games.
"He did everything. Scored goals. Made plays. Hit. He'd fight.
"Polite, genuine, respectful. You could just tell."
Interestingly enough, as the teenaged Jarome Iginla segued from junior hockey to that pair of playoff appearances and then into his first full season as a Flame, in 1996-97, the organization didn't seem so worried about his adapting to the NHL hurly-burly or the shift up in speed or even the physical erosion of clattering into grown men 82 times a winter.
No, they seemed more pre-occupied with his sleeping habits.
"This kid,'' laughed Calgary's head coach at the time, Pierre Page, "sleeps like a bear. Other guys nap. He hibernates.
"You worry about where other guys are at night and what they're doing. Not Iginla. The question is: 'Will you be able to get him out of bed?"
Twenty years on, Page reflects on the early days of a young man who in the interim fully earned his billing as the greatest player in Flames' annals.
"I just remember how much character he had, even as a kid,'' Page says now. "He didn't cut corners.
"He was like a Joe Sakic at that time. But he came to Calgary at a time they were getting rid of a lot of people, so it didn't add up the way it did for Sakic in Colorado. Turns out he was the right guy in the right place at the wrong time.
"So he ended up having to carry the flag by himself for a lot of years.
"I remember one day in the weight room, Jarome's lifting and Theo was there. Theo didn't do a lot of that conditioning stuff. He was so naturally gifted.
"And Theo told him: 'You don't have to do this --, you know.' I was there when Theo said it.
"Theo, remember, was a star, our best player. Jarome was just a kid.
"So I went up to Jarome afterwards and said: 'Uh, I think you know better, huh?'
"And - I'll never forget this - he just looked at me and said: 'Pierre, don't worry. I know what I have to do to be good.'
"Not for show. Not just to please the coach because it was the right thing to say. He knew."
Seated beside Iginla in the dressing room that first season was a 22-year-old defenceman, Todd Simpson, who, like Iginla, would go on to be a future captain of the Flames.
"I remember him being awfully young, innocent, always that big smile on his face,'' says Simpson today, retired for a decade and working as a realtor in Kelowna, BC.
"Everybody liked him. How could you not?
"That was my first full NHL season, too, but my third year pro. So I kinda helped walk him through it, what to expect, what to look out for. Oh, I knew he'd be good. For sure. Could I have envisioned him going on to do all the things he's done? Of course not.
"I was looking it up the other day. He had, what, 19 goals his first year (21, actually)? Even his first five years it wasn't as if he was lighting the world on fire. I mean, he was on the third line a lot of nights. Then he just sort of … took off.
"I remember back to that first year, though, even in practice, when he shot pucks they just seemed to go in. Almost always five-hole. I couldn't figure that out with the goalies … 'Don't you guys know he's going five-hole?' Over and over again.
"But he just had that quick a release and that good of a shooting eye.''
Since Simpson retired in 2006, he and Iginla, long-ago teammates, have kept in sporadic touch.
"I still see him about once a summer in Kelowna. We play our annual tennis match. I smoked him this year. Usually it's pretty close. But this year … absolute domination - 6-1, 6-2 or something like that. Ask him if he got some tennis lessons for Christmas this year, will you?
"I'm just so happy he's been able to play as long as he he has.
"I mean, I played 580 games over 10 years. You take injury into account and how good the league is and how long the seasons are and I think I did pretty well. But 1,500?
"That's just … crazy.
"Seeing him still going, after he's all he's accomplished, it'd kinda cool to say you were there in the beginning."
Yes, kinda, for all Calgarians seasoned enough to be able to make the claim. Jarome Iginla may be wearing invading colours these days, but the Saddledome is still his building. And this is still his town.
Which is why a visit remains a reason for celebration, especially as we get much nearer the end than that beginning, than Al Coates' 1:00 AM long-distance phone call to Kamloops.
"Looking back, that whole thing was such a whirlwind,'' reminisces Coates, peeling away the layers of two decades.
"Everything just kind of … fell into place. Fast.
"Really, when you sit back and think about it, those first 12, 13 hours, as crazy as they were, were the beginning of 20 years of something pretty special."