As Kaliko Teruya was coming home from her hula lesson on August 8, her father called. The apartment in Lahaina was gone, he said, and he was running for his life.

He was trying to escape the deadliest American wildfire in more than a century, an inferno in Hawaii fueled by powerful winds from a faraway hurricane and barely hindered by the state’s weak defenses against natural disasters.

Her father survived. But for Kaliko, 13, the destruction of the past week has reinforced her commitment to a cause that is coming to define her generation.

“The fire was made so much worse due to climate change,” she said. “How many more natural disasters have to happen before grown-ups realize the urgency?”

Like a growing number of young people, Kaliko is engaged in efforts to raise awareness about global warming and to reduce greenhouse gas emissions. In fact, last year she and 13 other young people, age 9 to 18, sued their home state, Hawaii, over its use of fossil fuels.

With active lawsuits in five states, TikTok videos that mix humor and outrage, and marches in the streets, it’s a movement that is seeking to shape policy, sway elections and shift a narrative that its proponents say too often emphasizes climate catastrophes instead of the need to make the planet healthier and cleaner.

Young climate activists in the United States have not yet had the same impact of their counterparts in Europe, where Greta Thunberg has galvanized a generation. But during a summer of record heat, choking wildfire smoke and now a hurricane bearing down on Los Angeles, American teenagers and twenty-somethings concerned about the planet are increasingly being taken seriously.

“We see what’s happening with climate change, and how it affects everything else,” said Elise Joshi, 21, the executive director of Gen-Z for Change, an organization she joined while she was in college. “We’re experiencing a mix of anger and fear, and we’re finally channeling it into hope into the form of collective action.”

The youth vote’s mounting frustration with the Biden Administration’s climate agenda is a wild card factor in next year’s presidential race. They are particularly livid that President Biden, who pledged “no more drilling on federal lands, period,” during his campaign, has failed to make good on that promise.

Young people are helping organize a climate march in New York next month, during the United Nations General Assembly. And their force is being felt even in deep-red states like Montana, where a judge on Monday handed the movement its biggest victory to date, ruling in favor of 16 young people who had sued the state over its support for the fossil fuel industry.

In that case, a lengthy fight resulted in a surprise victory that means, at least for now, that the state must consider potential climate damage when approving energy projects.

“The fact that kids are taking this action is incredible,” said Badge Busse, 15, one of the plaintiffs in the Montana case. “But it’s sad that it had to come to us. We’re the last resort.”

That mix of pride and exasperation is not uncommon among young climate activists. Many are energized by what they see as the fight of their lives, but also resentful that adults haven’t seriously confronted a problem that has been well understood for decades now.

“Do you think I really want to be on a stand saying, like, ‘I don’t have a future,’” said Mesina DiGrazia-Roberts, 16, another of the plaintiffs in the Hawaii case, who lives on Oahu. “As a 16-year-old who just wants to live my life and hang out with my friends and eat good food, I don’t want to be doing that. And yet I am, because I care about this world. I care about the Earth and care about my family. I care about my future children.”

In the Hawaii case, the youths have sued the state’s Department of Transportation over its use of fossil fuels, arguing that it violates their “right to a clean and healthful environment,” which is enshrined in the state Constitution. The state filed two motions to dismiss the case, but this month a judge set a trial date for next year.

A nonprofit legal organization called Our Children’s Trust is behind the Montana and Hawaii cases, as well as active litigation in three other states. A similar case it brought in federal court, Juliana v. United States, was thrown out by an appeals court in 2000, days before it was set to go to trial. But in June, a different judge ruled the case could once again proceed toward trial.

Vic Barrett, 24 and a resident of the Bronx, is one of the plaintiffs in Juliana v. United States and got interested in climate change a decade ago after learning about it in an after-school program not long after Hurricane Sandy inflicted widespread damage across the Northeast.

“I started understanding how low income and Black and brown people in New York were disproportionately impacted by Hurricane Sandy,” he said. “People like me are at the forefront of the climate crisis.”

“It’s absurd that while the Biden administration this year is celebrating the one-year anniversary of the I.R.A., it is actively opposing Juliana and working to expand drilling on federal lands,” said Zanagee Artis, 23, who quit a job at Goldman Sachs to spend more time working at Zero Hour, a climate nonprofit he co-founded while in high school.

Mr. Artis, who helped organize a youth climate march in 2018, is still sending people into the streets. Zero Hour is now recruiting people to attend the March to End Fossil Fuels, which will take place in New York on Sep. 17.

Chief among the frustrations of Mr. Artis and his cohort was the administration’s decision to approve Willow, a huge drilling project in Alaska. Early this year, TikTok erupted with calls for the White House to deny approvals for the project, thrusting the issue into the mainstream and giving thousands of young people a common cause. Creators juxtaposed images of Mr. Biden with collapsing glaciers, recorded tearful selfie videos and mashed up songs from “Encanto” with slide shows of cute animals.

Their efforts failed. In March, the administration approved Willow, which is set to produce crude oil for another 30 years. But the #StopWillow campaign, which garnered more than 500 million views on TikTok, showed that impassioned youth could shape the national debate.

“It was still a win,” said Ms. Joshi, who posted the first #StopWillow video on TikTok. “Millions of people were talking about why a project in remote Alaska was important to our health,” she said. “That base building is going to be used for future campaigns.”

Across the movement, there is an effort to combat “climate nihilism,” the fatalistic acceptance that nothing can stop runaway global warming. That sentiment, captured in the phrase “OK Doomer,” contributes to the slow pace of progress, they maintain.

Spinning the fear and frustration that many young people experience into positive action is a chief aim of Wanjiku Gatheru, 24, who founded an organization called Black Girl Environmentalist that is working to get more young people of color involved in the movement.

“Fear doesn’t motivate people toward sustainable action,” Ms. Gatheru said. “Providing solutions in the midst of discussion of a problem helps get people engaged.”

Enthusiasm for the climate movement is spreading in surprising ways. A group of young techno optimists who shun doomerism have embraced the label of “Decarb Bros.” And among Republicans, Millennials and members of Gen Z are far more likely than their elders to believe that humans are warming the planet and support efforts to reduce emissions, according to the Pew Research Center. Overall, about 62 percent of young voters support phasing out fossil fuels entirely, according to Pew.

On Maui, Kaliko and her family were trying to recover from the second natural disaster in five years. In 2018, flash flooding from Hurricane Olivia destroyed their home on the northern tip of the island. Now, the fire.

“We really need adults to wake up,” she said. “If we don’t fix this now, there’s not going to be a future.”