On a personal level, the candidate can’t quite connect with an incensed climate movement personified by Greta Thunberg, a 16-year-old Swedish activist who angrily chastised world leaders gathered at the United Nations last month, saying, “If you choose to fail us, I say we will never forgive you.”

Mr. Biden’s supporters seem incredulous that his record and proposals have not won young voters over.

“This is a guy who was introducing bills on climate change before this was on the radar screen of most politicians,” said Jake Sullivan, who served as Mr. Biden’s national security adviser in the White House. “He’s somebody who talks about the issue in an incredibly passionate and purposeful way.”

Mr. Biden’s campaign challenged the belief among many younger activists that the former vice president is not likely to make climate change a top priority if elected.

“There are some folks in the climate movement who are very vocal,” said Stef Feldman, Mr. Biden’s policy director. “There are also folks who are believers in the drastic efforts that we need to do to combat climate change who think Joe Biden is the best one equipped to address the challenge, because he has the experience of bringing other countries to the table.”

But other issues keep drowning out that message. Questions about Mr. Biden’s ability to energize voters on climate change come as national political attention is focused on accusations that President Trump put pressure on the Ukrainian government to investigate Mr. Biden and his son, Hunter Biden, who once sat on the board of a Ukrainian company, Burisma. (Despite Mr. Trump’s accusations of corruption on the part of the Bidens, no evidence has surfaced that the former vice president knowingly took any steps to help his son or the company.)

Trump supporters might focus on Hunter Biden’s monthly salary, as much as $50,000. Climate activists are more concerned about Burisma’s business: natural gas.