The tribal officials’ van deviated from the coastal highway, away from the Pacific, and onto a dirt path shaded by cedar and spruce trees. After climbing an old logging road, it emerged into a clearing high above the Shoalwater Bay Indian Reservation, half a square mile of vanishing oceanfront.

Despite the uneven terrain, the tribal leaders want to relocate to the remote hilltop where they were standing. “If you can believe it, this is the best building land we have,” said Quintin Swanson, the tribe’s treasurer. He estimated that moving up the mountain would cost half a billion dollars.

As climate change worsens, tribes like Shoalwater Bay find themselves caught between existential threats and harsh financial arithmetic. Some tribes, who were relegated to marginal land by the US government more than a century ago, are now attempting to relocate to areas better protected from extreme weather but lack the funds to do so.

In response, the Biden administration appears to have established the first program in American history aimed specifically at assisting communities threatened by climate change. The Department of the Interior is currently deciding which tribes will receive funding this year — and which will have to wait even longer as their land sinks deeper into the sea.

That decision, which is expected soon, is likely to have far-reaching consequences beyond Indigenous Americans, by establishing a model for other agencies to emulate.

The federal government has been quietly attempting to shift its approach away from endlessly rebuilding after disasters and toward assisting the most vulnerable communities in fleeing vulnerable areas. Moving is, however, costly, and as disasters worsen, the demand from communities to relocate will only grow, straining the government’s ability to pay for it.

As a result, the new program serves as both a test case and precedent for perhaps the most difficult dilemma confronting the United States as it adapts to climate change: how should the government decide where to help first?

Mr. Newland, a resident of the Bay Mills Indian Community, admitted that the program will not provide funds to every tribe in need. Even the winning tribes will not receive all of the funds they require.

For centuries, the United States forcefully relocated Native Americans, with disastrous consequences that continue to this day. Many tribes were relocated to less hospitable land, making them more vulnerable to extreme weather.

In 2016, the federal government attempted a different type of relocation. It provided $48 million to relocate Isle de Jean Charles, a coastal Louisiana village sinking into the Gulf of Mexico, inland. The majority of residents belonged to the Biloxi Chitimacha-Choctaw tribe.

That relocation was a one-time project intended to serve as a model for towns that could no longer be protected from the effects of climate change.

However, relocation, also known as “managed retreat,” by experts, is gaining popularity. Last year, Congress appropriated $130 million to the Interior Department’s Bureau of Indian Affairs to be spent over five years to assist tribes in relocating.

The funds will be distributed in the form of competitive grants of up to $3 million per year. This year, the bureau will spend $25.8 million on community relocation.

The New York Times obtained a list of at least 11 tribes that have applied for relocation grants through a public records request. Five of these tribes are concentrated within about 100 miles of each other on Washington State’s Olympic Peninsula, making it the site of one of the most significant experiments in US climate adaptation policy.

Hotter air means more intense rainfall, which fills the area’s rivers and streams as the planet warms. As storms intensify, coastal communities become vulnerable to inland flooding as well as coastal surges. “It’s kind of a double whammy,” Dr. Bond explained.

Much of the reservation is a broad coastal marsh that is prone to erosion. In a typical year, the ocean moves another 100 feet inland.