SAN DIEGO — What once appeared to be the apex of the history of the San Diego State men’s basketball program occurred just over three years ago.

After a 26-0 start, the Aztecs were 30-2, ranked sixth in the Associated Press poll and projected to be seeded No. 1 or 2 in the N.C.A.A. tournament. They were well on their way toward fulfilling the shared vision of Steve Fisher and Brian Dutcher, the two men whose brilliant construction reversed the course of a program that for decades was known for chronic underachievement.

Then the 2020 tournament was canceled because of the coronavirus pandemic. Everyone went home, sad and scared.

“Sometimes we take for granted just going and losing in the first round,” Dutcher, who is in his sixth season as the Aztecs’ head coach after 27 years assisting Fisher at Michigan and San Diego State, said recently. “Just to have a chance to play would have meant the world to those guys.”

Schools like San Diego State usually do not get a second chance to catch a dream. That is what makes its surge in this year’s N.C.A.A. tournament both remarkable and inspiring. And the Aztecs are not taking a second for granted.

Set to face Florida Atlantic in a national semifinal Saturday in Houston, San Diego State is not only in its first Final Four, it also is the first Mountain West Conference team to advance this far.

Before stunning top-seeded Alabama and then slipping past Creighton last weekend, the school had never been beyond the round of 16. Just three of its key players — guard Adam Seiko and the forwards Nathan Mensah and Aguek Arop — are left from that 2019-20 team, and each is playing only because of N.C.A.A. rules allowing those affected by the pandemic an extra season of eligibility.

“It’s a blessing,” Seiko said. “It really is a blessing.”

So, too, is it for those with ties to San Diego State who have lived through the growing pains. The school has just one national championship in anything — men’s volleyball in 1973 — and then eliminated that sport because of budget cuts in 2001.

The football program experienced some glory in the 1960s with Air Coryell — the eponymous high-powered passing offense of Coach Don Coryell, who will be posthumously inducted into the Pro Football Hall of Fame this August — and again briefly in the early 1990s with the star running back Marshall Faulk. But the basketball program mostly had remained lost in the wilderness.

It wasn’t for lack of effort. San Diego State poached Jim Brandenburg, the Wyoming coach, after the Cowboys upset U.C.L.A. en route to a round of 16 appearance in 1987. But that became a disaster and Brandenburg was fired in his fifth season.

The Aztecs explored the possibility of hiring Jerry Tarkanian when he was in exile from college basketball after leaving the University of Nevada-Las Vegas amid a battle with the N.C.A.A. in the early 1990s, but he was too controversial for school administrators.

“It’s been a long, arduous journey for the university,” Michael Cage, a star San Diego State forward from 1980-84 who played 15 seasons in the N.B.A. and now is a broadcaster for the Oklahoma City Thunder, said this week.

Cage added: “There’s no prouder alumni in the world than me right now. Because when I got there, the coaching staff didn’t even have offices. They had trailers across the street from Peterson Gym.”

The Aztecs played some of their home games in the 1980s and ‘90s in Peterson Gym, an on-campus building that essentially was a glorified high school facility. It was a sight to behold in December 1992, when a 22nd-ranked U.N.L.V. led by Coach Rollie Massimino rolled in like rock stars and played in the sub-Division I structure in front of 3,538.

The rest of the home schedule unspooled at the city’s sports arena.

“I had to drive almost half an hour for my own home games,” said Cage, the highest N.B.A. draft pick — No. 14 overall in 1984 — from San Diego State. “And we didn’t have a practice facility, we just had Peterson Gym. I spent a lot of my time after practice on the basketball courts outside shooting at night because somebody else had to get in the gym.”

Viejas Arena opened in 1997, giving the program an on-campus home commensurate with other Division I programs. Fisher and Dutcher, in part because they could use the facilities — including a practice gym — to their benefit in recruiting, arrived two years later. At that point, the Aztecs had played in only three N.C.A.A. tournaments in three decades. The program was so decrepit that Fisher’s first team was 5-23 overall and winless in the Mountain West.

Now, Dutcher has been on the sidelines either as an assistant or the head coach for 21 of the program’s 24 tournament games, and for all 10 of its victories.

Until Kawhi Leonard, who is now with the Los Angeles Clippers, the best known Aztecs basketball player other than Cage was Tony Gwynn, the Baseball Hall of Famer. A point guard from 1977-81, Gwynn remains the school’s career assists leader (590) and coached the school’s baseball team after his retirement from playing.

“Completely different universes, quite frankly,” said Tony Gwynn Jr., who played baseball for his father at the school from 2000-03 and now is the Padres’ radio analyst after a major league career of his own. “I remember Coach Dutcher personally walking around campus and inviting students to the games. He was on campus all the time, it felt like.”

Even with Leonard and, finally, a stuffed arena with a raucous student section, the Aztecs felt like they were capable of more. What they thought was a winnable game ended with a loss to Connecticut in the round of 16 in the 2011 tournament in front of a friendly crowd in Anaheim, Calif. It was a contest that turned on two questionable technical foul calls against San Diego State, including one against Leonard. UConn won the national title that season.

UConn, playing Miami in the other semifinal Saturday, is lurking in Houston, but for now it is a 35-3 Florida Atlantic team on which the Aztecs are focused.

“That would be like us with our 30-2 team, people asking, ‘Do they look like a Power 5 conference team?’” Dutcher said. “We were 30-2 and had the best record in the country, and they’re the same way right now. They have to be respected for that.”

San Diego State’s 31 wins is tied for third in Division I. And since the start of that 2019-20 season, the Aztecs’ 82.9 winning percentage ranks third behind Gonzaga and Houston.

The Aztecs make their bones on defense, and in four games this tournament are holding opponents to 17 percent shooting from 3-point range (16 for 94).

“It’s a testament to the culture that Coach Fisher and Coach Dutcher built at S.D.S.U.,” Gwynn Jr. said, referring to the team’s two 30-win campaigns in four years. “Those type of seasons don’t come around even for blue bloods all the time, right?”

Where they once rarely filled the tiny Peterson Gym, the Final Four-bound Aztecs were greeted by students and well-wishers upon their return to campus from the South Regional in Louisville, Ky., at 1 a.m. Monday. Guards Lamont Butler and Darrion Trammell, who hit the winning free throw in the regional final against Creighton, spoke Tuesday of posing for selfies and receiving congratulations during a trip to the beach later that day. Cage, who has been excused from two Thunder broadcasts this weekend so he can attend the Final Four, said he has heard from more Aztecs fans this week than ever before.

The way Dutcher figures it, the basketball program now is the “front door” to a “great university.”

“We can’t say going to the Final Four is the end-all,” Dutcher said. “It’s the beginning. So now we have to try to find a way to win two games and hang a championship banner.”