LOS ANGELES — On the cusp of his 19th N.B.A. season, Carmelo Anthony belongs to a new team but harbors the same ambitions: winning his first championship. In that regard, he is not alone on the Los Angeles Lakers, a collection of veterans who will form one of the league’s most curious experiments.

“We have too much experience on this team to think anything other than we’ll figure it out,” Anthony said. “But it all takes time.”

After a winless preseason, the Lakers will get going in an official capacity on Tuesday night, when they play their season opener against the Golden State Warriors, a franchise that has recently gone about its business in a decidedly different way.

While the Lakers have been a tear-down project — LeBron James, who signed with the team in 2018, is the longest-tenured player on the roster — Golden State has been busy remodeling while keeping intact the essential core from its not-so-distant championship era, all in the hope of staging a resurrection with the help of some new pieces.

Two teams. Two approaches. And an early-season, but much-anticipated, litmus test at Staples Center on the viability of each.

“I think we’ll be ready,” Anthony said. “You can feel it.”

The Warriors — remember them? — are running it back with Stephen Curry, Draymond Green and, eventually, Klay Thompson, whom the team expects to return by late December or early January after he missed the past two seasons with injuries. Thompson tore the anterior cruciate ligament in his left knee in the 2019 finals, then ruptured his right Achilles’ tendon last November.

“It doesn’t work without Klay,” Curry said in an interview last week. “So there’s definitely anticipation. And we feel like we’ll have three seasons in one this year: this first chapter until he gets back, reintegrating him into the fold, and then the playoff chase down the stretch. So there’s a lot to look forward to.”

Without Thompson — and largely without Curry, who broke his hand and missed all but five games — Golden State hibernated through the 2019-20 season, finishing with the worst record in the league. Last season, as the team continued to groom prospects like Jordan Poole, a first-round draft pick in 2019, and Juan Toscano-Anderson, who came out of the G League, the Warriors went 39-33.

Now Golden State is nearly whole. And the team has welcomed the reappearance of a familiar figure: Andre Iguodala, a key cog in the team’s five straight trips to the finals, from 2015 to 2019, which produced three championships.

“We built something special here,” said Iguodala, who has rejoined Golden State after spending most of the past two seasons with the Miami Heat.

While Iguodala was gone, Golden State experienced its share of turbulence. But the franchise maintained a sense of stability. Curry and Green were still around. Thompson would be back at some point. And Steve Kerr, now entering his eighth season as the team’s coach, was at the helm. The pieces were there. It would just take some time for them all to coalesce again.

“Our expectations are definitely higher this year than they have been the last couple of years,” said Kerr, whose team went 5-0 in the preseason. “It’s a really fun group to coach.”

The Lakers will be playing under an even brighter spotlight after overhauling their roster (again) this summer. They signed Anthony, traded for Russell Westbrook and acquired veterans like Kent Bazemore, DeAndre Jordan, Dwight Howard and Rajon Rondo while jettisoning the bulk of their personnel from last season. Gone are many of the role players from their championship run in 2020: Kyle Kuzma, Alex Caruso, Kentavious Caldwell-Pope.

The Lakers are not big on continuity, demonstrating a willingness to sacrifice draft picks and young players for name-brand stars of a certain vintage. If there is urgency, it stems in large part from the fact that James is 36 and has struggled with injuries in recent years. No athlete can operate at the height of his powers forever, not even James. And so the Lakers have gone about mortgaging their future in pursuit of another championship now — if they can create chemistry in short order while avoiding more health problems.

“I think our basketball I.Q., our talent and our skill will, for the most part, get us there,” Anthony said, “and then, the cohesiveness of being together and playing together will take us over the top. We understand where we want to be and where we’re going to be, but we’re not there yet.”

The team has acknowledged that it will be a work in progress. As James put it before the start of training camp, “I don’t think it’s going to be like peanut butter and jelly to start the season.”

Any mention of preseason basketball ought to come with the disclaimer that the games are fairly meaningless. But the Lakers did go 0-6, which was enough to raise some important questions: Is this a hodgepodge roster? Can a team this old withstand the rigors of an 82-game regular season? And, perhaps most important, can Westbrook and James, two ball-dominant players, coexist in a productive way?

Frank Vogel, the team’s coach, said he had no such concerns.

“There’s definitely a willingness for those guys to share and sacrifice,” he said, adding, “It’s tough to get 15-plus-year vets to be completely serious about the preseason.”

For his part, James said Monday that he had fully recovered from the ankle injury that slowed him toward the end of last season — “I didn’t do much basketball for the first two months of the summer,” he said — and that he was ready for a fresh start, one that will come against an opponent that, unlike the Lakers, hopes to reach into its past.