Eight-year-old L.J. Jones thought his grandfather Ralph Simpson had been keeping a secret from him. So he demanded answers.

“Grandpa, can I ask you something?” Simpson, 73, recalled his grandson saying, imitating the young boy’s serious tone.

“Grandpa,” the boy said. “Somebody told me you was famous.”

Simpson had to laugh. After all, he is not the most famous Ralph; that might be Ralph Lauren, or Ralph Waldo Emerson. Nor is he the most famous member of his family; that would be his daughter, the Grammy Award-winning soul singer India.Arie.

“Grandpa’s not famous,” Simpson told his grandson. “I played for the Nuggets and played professional basketball.”

Still, L.J. wanted to know, “Why you didn’t tell me?”

Simpson started on the 1975-76 Denver Nuggets in the American Basketball Association. They were the only Nuggets group to make it to a championship round until this year’s team reached the N.B.A. finals. The 1975-76 squad lost the A.B.A. championship series in six games to Julius Erving’s New York Nets. The A.B.A. and N.B.A. merged before the 1976-77 season, and the Nuggets spent the next 47 years in basketball purgatory, with a few teams that inspired confidence but none that reached the finals.

Now, the Nuggets are one win away from the first championship in franchise history. As they try to close the series at home Monday in Game 5 against the Miami Heat, they’ll be cheered on by some of the men who played for that A.B.A. title.

“It has been so cool because the Nuggets currently making it to the finals has brought out a lot of memories for people that didn’t realize that Denver had an A.B.A. team that went to the finals,” said Gus Gerard, 69, a backup player on the 1976 finals team. He added, laughing: “The only frustrating thing for me is they’re showing all these highlights and it’s always the same ones of Julius Erving, the great Dr. J, dunking on us left and right.”

Like today’s Nuggets, the 1976 team routinely demoralized opponents with its near unstoppable offense, but often felt like the underdog. The older Denver team also toiled in obscurity for much of the season.

A Sports Illustrated article on May 29, 1976, lamented that “Denver games are not on national television,” and that “Denver box scores do not appear on most sports pages.” The article noted that some “large media outlets” still referred to the Nuggets as the “Denver Rockets,” which had been their name until 1974. The franchise changed its name because it planned to move to the N.B.A., where the name Rockets was already taken by Houston.

The 1975-76 Nuggets had the best record in the A.B.A. They were led by three future Hall of Famers: Bobby Jones, Dan Issel and David Thompson. Nicknamed Skywalker, Thompson had been the top draft pick in 1975 in both the A.B.A., by the Virginia Squires, and the N.B.A., by the Atlanta Hawks. But he chose to sign with the Nuggets instead.

“David Thompson, man, I used to get myself standing and watching him when I’m in the game,” said Byron Beck, 78, who played for Denver in all nine of its A.B.A. seasons and its first in the N.B.A. “You know, you catch yourself, ‘Oh!’ and he’s already gone doing something spectacular.”

They were coached by Larry Brown, who won an A.B.A. championship as a player in 1969 with the Oakland Oaks, a men’s N.C.A.A. Division I basketball championship as a coach at Kansas in 1988 and an N.B.A. championship as a coach in 2004 with the Detroit Pistons.

In 1975-76, the A.B.A. was contracting, having gone to seven teams from 10, and had only one division. The All-Star Game pitted the Nuggets against All-Stars from other teams.

Claude Terry, then a Nuggets reserve guard, said he remembered going to the All-Star Game with his wife and their two children in a station wagon. He said he was “probably wearing old Levi’s and shoes that didn’t get messed up in the snow.”

He added: “I don’t remember even being interviewed during the game.”

That season, the Nuggets packed their new McNichols Arena, which opened in 1975, with the pending N.B.A. merger in mind, and was demolished in 2000. Gerard remembered being swarmed for autographs and invited for free meals at restaurants, like the Colorado Mine Company.

“They had, like, the best prime rib you ever tasted in your life,” Gerard said.

Amid the excitement, there was also uncertainty. Preparation for the merger with the N.B.A. weighed on the players, who knew that only four of the seven A.B.A. teams would survive it. The Nuggets, Nets, Indiana Pacers and San Antonio Spurs continued in the N.B.A.

“Most of us didn’t have no-cut contracts,” Terry said, adding that players were “not nervous, but just trying to figure out what was next.”

Terry said coming changes kept the players from appreciating what it to meant to play in the final A.B.A. season. Had there been social media at the time, Terry said they might have paid more attention to the significance.

The Nuggets played the Kentucky Colonels in the first round of the playoffs and won in seven games. Then they faced the New York Nets, who had the best player in the series in Erving. Denver lost Game 1 at home. Facing elimination at home in Game 5, they won despite 37 points from Erving. Simpson and Issel led the team with 21 points each, and Gerard had 12 off the bench.

If they could force a Game 7 in Denver, they were sure they could win it. But Erving led a furious fourth-quarter comeback in Game 6 to win the game and the championship.

“We should have beat them,” Simpson said. “We had a better team. Even Julius Erving thought we did. But they got out on us.

As the years passed, though they stayed in touch with each other, some members of that Nuggets team became increasingly disconnected from the franchise. Most of them moved out of Denver, and went on to have careers outside of basketball.

Thompson and Gerard went through well-publicized battles with drug addiction. Gerard later became a substance abuse counselor. He now works for the Fayette County government in Pennsylvania and still helps people recovering from addictions. Thompson participates in Nuggets fan events and attended Game 2 of the finals in Denver. He and Jones, who played for the Nuggets until 1978, started a religious nonprofit in North Carolina.

Issel remained the most connected to the franchise. He played for the Nuggets until 1985, then returned as a broadcaster a few years later. Issel coached the Nuggets twice, the second time also serving as the team’s president. He apologized in 2001 after using a racial epithet toward Mexican people in response to a fan’s taunt, then resigned shortly afterward.

This year, with his five grandchildren in tow, Issel went to Game 1 of the finals, which Denver won at home, 103-94.

Simpson has been watching the games at home, and invites his grandchildren for a pizza party to watch with him. He didn’t get to play for Denver in its debut N.B.A. season because he was traded to Detroit, but the Pistons traded him back the next season. He stays in touch with A.B.A. and N.B.A. alumni by being active with the National Basketball Retired Players Association.

Denver’s 47-year drought before returning to the finals is perplexing to him.

“We’ve had some really good players,” said Simpson, who coached at a small school briefly and used to be a pastor in Denver. “I’m really surprised we haven’t won a title yet.”

To win the franchise’s first, this year’s Nuggets have tried to focus narrowly on the task before them. Much like how the A.B.A. Nuggets weren’t thinking about history, these Nuggets aren’t using the franchise’s long drought as inspiration.

“I don’t know much about it,” Denver’s Bruce Brown said. “Who was on that team?”

He said he tries not to think about what a championship would mean for the franchise and for the city of Denver.

“Then I’ll get too happy, too anxious,” Brown said. “I just try to stay in the moment.”

The 1975-76 team’s try at making history has been obscured by the years, but Brown and his teammates are on the verge of completing the journey they began.