Of course, the vast majority of sports fans in America didn't know or care who Don Shula was. He was just some greenhorn no-name who probably was in way over his head by trying to coach pro football stars like John Unitas, Raymond Berry, Tom Matte and Gino Marchetti.
Well, 30 years have come and gone since then, and things have changed. But Shula still is coaching pro football players. That obscure young man who got his chance in 1963 will soon have more victories than any coach in NFL history. If the Miami Dolphins defeat the Kansas City Chiefs on Sunday, Shula will tie the legendary George Halas for the top spot on the NFL list with 324 victories.
"Sure, it will be special," Shula said of the record. "Who doesn't want to be known as the best ever? But I never spent much time thinking about it. Those numbers just add up over time. You do your best every day, every week, every year. The milestones are a byproduct of hard work."
No matter what the final victory total ends up being for Shula, many experts believe it is a record that never will be broken.
"Whatever mark Don ends up putting on the board, it will last forever," said former Chicago Bears coach Mike Ditka. "Nobody's going to touch it."
Even Shula believes his victory total will be difficult for another coach to equal.
"In this day and age with so many coaches not staying around very long, it's hard to conceive anybody breaking it," Shula said. "You see Tom Landry and Chuck Noll leave, then Mike Ditka and Joe Gibbs. You realize how tough it is to stay in this profession."
Winning often is the most impressive thing about Shula's record. Not only is he on the verge of winning more games than any coach in NFL history, Shula also has won a higher percentage of games than any other active coach.
His 323-152-6 record is a .676 winning percentage. His six Super Bowl trips are more than any other coach, and he has had only two losing seasons in 31 years (6-8 in 1976 and 6-10 in 1988). Halas won 324 games in 40 seasons. Shula will do it in 31.
Former Oilers-Saints coach Bum Phillips, who had a way with words, once said of Shula: "He can take his'n and beat your'n, or take your'n and beat his'n."
"Vince Lombardi wrote the book on coaching," Modell said. "But Don Shula edited it."
Some of the best players in the history of the game have lived through that editing process over the last four decades. Most of them will tell you, in the early years, Shula was the surly tyrant that typified coaches of the era.
"My main goal every year at training camp was to keep him from chewing me out," said former Miami center Jim Langer, a member of the Hall of Fame. "I would do anything to keep him from yelling at me."
Some of Shula's former players say the coach has mellowed over the years.
"You don't see the frothing and spitting on the sidelines like we used to see from him," said former Miami running back Mercury Morris.
Shula, almost 64, admits he has changed some over 31 seasons, which probably is the reason he has survived the NFL battles for so long.
"I'm a little more willing to listen," he said. "I'm not as apt to plunge straight ahead and say, 'This is the only way.' But some things will never change. Honesty is the heart of my success. I don't play games with players. You always need discipline, and there can only be one boss. That's me."
His temperament may have changed a little, but Shula always has been a man with tunnel vision and a single purpose to winning in football.
"He would show us pieces of game films over and over," Langer said. "So we started counting how many times we had to watch the same play. The record is 72 times. We actually watched one play 72 times."
Another example of Shula's mellowing came when tight end Marv Fleming became one of the first athletes to wear an earring. Fleming is a free-spirit who loved to try to get Shula riled up.
Fleming walked into Shula's office when he reported to training camp, and the two men talked about football for a few minutes with no response from Shula about the new jewelry.
Finally as Fleming started to walk out, he said, "Coach, don't you notice something different about me?"
Without looking up from his playbook, Shula calmly replied: "Yeah. One of your earrings is missing."