Outside a small coal town in southwest Wyoming, a multibillion-dollar effort to build the first in a new generation of American nuclear power plants is underway.

Workers began construction on Tuesday on a novel type of nuclear reactor meant to be smaller and cheaper than the hulking reactors of old and designed to produce electricity without the carbon dioxide that is rapidly heating the planet.

The reactor being built by TerraPower, a start-up, won’t be finished until 2030 at the earliest and faces daunting obstacles. The Nuclear Regulatory Commission hasn’t yet approved the design, and the company will have to overcome the inevitable delays and cost overruns that have doomed countless nuclear projects before.

What TerraPower does have, however, is an influential and deep-pocketed founder. Bill Gates, currently ranked as the seventh-richest person in the world, has poured more than $1 billion of his fortune into TerraPower, an amount that he expects to increase.

“If you care about climate, there are many, many locations around the world where nuclear has got to work,” Mr. Gates said during an interview near the project site on Monday. “I’m not involved in TerraPower to make more money. I’m involved in TerraPower because we need to build a lot of these reactors.”

Mr. Gates, the former head of Microsoft, said he believed the best way to solve climate change was through innovations that make clean energy competitive with fossil fuels, a philosophy he described in his 2021 book, “How to Avoid a Climate Disaster.”