But Mr. Benioff, a tech mogul and environmental philanthropist, felt sure he had found a climate change solution that even President Trump could love: Planting trees.

Never mind that the idea came from former Vice President Al Gore, who has demanded Mr. Trump’s resignation over his energy policies. Never mind that Mr. Trump has begun the yearlong process of withdrawing America from the Paris Agreement on climate change, mocked Greta Thunberg, the teenage climate activist, and worked to eliminate every regulation aimed at reducing planet-warming emissions.

The idea of planting one trillion trees had one enormous political advantage: It was practically sacrifice-free, no war on coal, no transition from fossil fuels, no energy conservation or investment in renewable sources of power that Mr. Trump loves to mock, like the windmills that cause cancer or the solar panels that are not “strong enough.”

“I just knew this is a really good idea. I said I will pitch it and see what happens,” Mr. Benioff said. “Even my chief of staff said to me, ‘You’re not going.’”

How the trillion trees initiative migrated from Mr. Benioff’s PowerPoint presentations to the president’s pronouncements, first at the World Economic Forum in Davos, Switzerland, last month, then his State of the Union address last week, is a study in ad hoc policymaking at the Trump White House. A personal appeal from a celebrity voice got the idea past traditional gatekeepers. A back channel through Jared Kushner, the president’s son-in-law, gave it life, and a re-election campaign that has sought to soften some of Mr. Trump’s sharper edges ensured its publicity.

It is far from clear that the United States government will actually plant any trees, or that a trillion trees would do much in the near term to stop the worst effects of planetary warming. Tom Crowther, an environmental scientist and an author of the study that sparked the movement, cautioned that the full benefits would not be seen for about 100 years, when most of the new trees would reach full maturity. During that time, he said, the world needs to drive down fossil fuel emissions.

“If tree planting is just used as an excuse to avoid cutting greenhouse gas emissions or to further limit environmental protection, then it could be a real disaster,” said Dr. Crowther, who studies ecosystem ecology at ETH Zurich.

But such details might be beside the point for a White House initiative that is heavier on politics than science. One senior administration official described the tree initiative as one the president believes will “bring people together.”

“We’re committed to conserving the majesty of God’s creation and the natural beauty of our world,” Mr. Trump told investors and world leaders in Davos.

Despite his longstanding antagonism toward climate science, Mr. Trump in recent months has struck a softer tone on the topic. In a meeting with President Emmanuel Macron of France in December, he said climate change was “very important” to him. He recently denied the undeniable fact that he ever declared global warming a hoax.

He even said he was reading a book on the topic. (The book, according to the White House, was, “Donald J. Trump: An Environmental Hero” by Ed Russo, a former consultant to the president).

The president’s commitment to a global effort to plant one trillion trees by 2030 surprised even White House officials who work on environment policy. Mr. Trump never uttered the phrase “climate change” in his pledge. He described it instead as a plan “to protect the environment.”

Yet the science behind it is centered on planetary warming. As trees grow, they absorb the carbon dioxide emissions that drive climate change. According to researchers at ETH Zurich, worldwide reforestation with 1.2 trillion trees could reduce atmospheric carbon in the atmosphere by about 25 percent.

And with polls showing many young Republicans breaking with their party on climate change, political strategists described the initiative as part of an effort to steer Mr. Trump toward more environmentally friendly messaging without abandoning the development of more planet-warming fossil fuel energy.

“It’s obvious the president’s team understands this is a weakness for him right now given the rhetoric he’s used, the dismissal of climate science and all of the executive actions that are consistent with that rhetoric,” said Carlos Curbelo, a former Republican congressman from Florida who championed a carbon tax when he was in office.

The shift is happening across the Republican Party, which has inched over decades from denying the existence of climate change to saying it was part of a natural cycle to dismissing it as unstoppable to considering modest policy responses. On Wednesday, House Republicans are expected to introduce the first of a three-part package of climate change legislation. The bills will focus on funding the capture and storage of carbon dioxide emissions from fossil fuel plants; developing clean energy; and conservation measures like planting trees.

“Trees aren’t the only solution to addressing the climate issue, but I’ll say they are by far one of the best solutions,” said Representative Bruce Westerman, an Arkansas Republican who is developing legislation to bring the United States into the trillion tree plan.

“It’s a big goal to plant a trillion trees globally, but I think the world needs a big solution,” Mr. Westerman, a Yale-educated engineer and forester, said.

It remains unclear what the Trump administration is committing to do in joining the trillion tree plan. While one senior administration official said this week that the White House was busy preparing a tree-planting target, another noted that the $4.8 trillion budget issued Tuesday did not mention the plan.

This is not the first time a back channel has been used to let a big name promote the climate cause. During Mr. Trump’s presidential transition, Mr. Kushner and his wife, Ivanka Trump, brought Mr. Gore and Leonardo DiCaprio to Trump Tower to press for action on climate change — to no avail.

Those who deny the established science of climate change are confident Mr. Trump’s heart is with them. They point to another part of his speech in Davos, in which he railed against the “prophets of doom” who warn of climate catastrophes.

“Donald Trump is as militant against the climate hysteria as ever,” said Steven J. Milloy, a member of Mr. Trump’s transition team who runs a website promoting the false theories that climate change alternately isn’t real or harmful.

Mr. Benioff, in a telephone interview, said he decided to take a chance anyway. Mr. Gore had bent his ear last summer about emerging research into reforestation and climate change. After discussions with scientists at the Benioff Ocean Initiative, a program at the University of California, Santa Barbara, he was hooked.

“I realized this looks like a practical, actionable thing,” he said.

He discussed it with other scientists, such as Jane Goodall, the English primatologist, as well as financiers, hoping to rally governments and companies around the initiative at the World Economic Forum.

Mr. Benioff has known Mr. Kushner since before Mr. Trump took office and has worked with Ivanka Trump on issues like job training. He traveled to Washington to discuss the tree initiative with Mr. Kushner in October.

“People think something that’s actually not true, which is that they’re not interested in hearing new ideas or hearing science,” Mr. Benioff said of the Trump administration.

“Trees are the ultimate bipartisan issue,” he added. “Everyone is pro-tree.”

Mr. Gore applauded Mr. Benioff for getting the issue on President Trump’s radar. “I would not have expected him to have any success on that,” he said in an interview.

But he was skeptical. “I don’t have any trust in the Trump administration’s approach to climate because no one can be deemed as serious on the climate crisis unless they’re in favor of emission reductions,” he said.

Dr. Crowther was more optimistic. Speaking from a camper in the Moroccan desert where he half-joked he had gone to escape the attention his work has spurred, he said, “If restoration can be socially and ecologically responsible, I think it poses a really exciting opportunity for bipartisan leadership.”

Mr. Curbelo, the rare Republican politician who has embraced a politically difficult response to climate change, conceded that tree planting and carbon capture programs were modest at best, and both parties would need to negotiate ambitious emissions cuts.

“However,” he added, “that was impossible when Republicans weren’t even at the table.”