Along the southeastern edge of Oklahoma, where expansive cattle ranches and empty storefronts dot the landscape, the lack of high-speed internet service has become a daily frustration for residents.

Wanda Finley, a fourth-grade teacher in Sawyer, Okla., said the satellite service at her home was often too slow to use, and it sometimes went out for days. She cannot schedule medical appointments, request prescription refills or pay her bills online until she gets to work. Nearly every weekend, she drives about 40 minutes to school to prepare her weekly lesson plan because it can take minutes for a single web page to load at home.

“I’m hoping it will change,” Ms. Finley, 60, said, sitting in her home on a recent afternoon.

If President Biden gets his way, Ms. Finley and her neighbors will benefit from a $42.5 billion program to expand fast internet access across the country. The funding, which was included in the 2021 infrastructure law, is part of an initiative that has high ambitions: to provide “affordable, reliable high-speed internet” access for every home and business by 2030.

The effort is meant to close the “digital divide” by ensuring that all Americans can connect to fast internet, given the critical role it plays in economic opportunities, education, health care and other areas. The Biden administration has also invested more than $22 billion in other programs to build broadband networks and reduce the cost of internet bills.

The lack of broadband infrastructure is particularly problematic in rural areas, where internet service is often unavailable or limited. Roughly 24 percent of Americans in rural areas lack high-speed internet service as defined by the new program, compared with 1.7 percent in urban areas. Research has shown that internet connectivity can fuel economic growth in rural areas, helping to create jobs, attract workers and increase home values.

Attempts to get broadband to everyone are not new: The federal government has already pumped billions into efforts that have had mixed results. Biden administration officials have said the new program, coupled with other federal and state funding, would be enough to finally reach everyone who lacked high-speed internet access.

But some state officials and industry analysts remain wary and have raised concerns about whether the funds will achieve all of the administration’s goals.

In part, that’s because of the sheer cost of deploying broadband infrastructure in rural and sparsely populated areas. It can be expensive to lay fiber-optic cable when homes are spread far apart and terrain challenges make it difficult to dig in the ground. Labor shortages could further drive up construction costs and delay projects.

There are 8.5 million “unserved” and 3.6 million “underserved” locations across the country, according to Federal Communications Commission data. Each state received a minimum of $100 million from the $42.5 billion bucket, plus additional funds based on its number of unserved locations. States must first address areas that have no or insufficient internet service, and can then use funds to build out in underserved areas. Remaining funds can be used on community institutions and then issues such as affordability.

The success of the initiative is expected to vary across states. Some, like Louisiana and Virginia, have already said they anticipate covering every unserved and underserved location. Others have expressed more skepticism about the funding’s reach.

Edyn Rolls, Oklahoma’s director of broadband strategy, said that it was unlikely that the state, with its large rural population, would have enough funds to reach every underserved location, and that covering all of the unserved areas could be a challenge.

State officials said that recent versions of the F.C.C.’s map showing available internet service across the country had improved, but it could still be overstating coverage. Local governments and providers will be able to challenge existing data, but state allocations are already set, meaning funds would have to be stretched further if officials identified more locations that lacked high-speed service.

Ms. Rolls said there was a “real potential” that such a scenario could develop, adding that officials have heard from residents who say there is “definitely an overstatement of service.” And even though she said fiber would be a better long-term investment, a mix of technologies would have to be deployed to reach every unserved location.

Even with the grants, companies might not find it profitable to build everywhere. Robert Osborn, director of California’s communications division, said some locations in the state, which is geographically diverse with large areas that are hard to reach, are not likely to receive any provider interest. To attract bidders, Mr. Osborn said, the state could in some cases reduce the requirement for providers to cover at least 25 percent of a project’s price tag, but that risks drawing money away from other projects.

“It’s not as simple as giving money to a major internet service provider and saying, ‘Go build there,’” Mr. Osborn said.

Evan Feinman, the director of the National Telecommunications and Information Administration’s $42.5 billion program, said officials were confident that the federal and state funds would be enough to cover every unserved and underserved location, meaning every American would have access to an internet speed of at least 100 megabits per second for downloads and 20 megabits for uploads.

Still, he said some projects could take as much as five years to complete, and he anticipated construction would not start until late 2024. Although he said most locations would receive fiber connections, he expected others would be covered by fixed wireless or satellite technology.

Satellite is not considered reliable under the program rules, but Mr. Feinman said some services were better than others, and states could use funds for satellite equipment and service for a handful of remote locations. Starlink, a satellite technology made by Elon Musk’s SpaceX, is considered to be more reliable, but the hardware costs hundreds of dollars, and it can take months to get off wait lists.

The funding’s reach will matter for Americans who have long lacked high-speed internet access. Ms. Finley said she wanted to assign homework that involved more online research, because it would accelerate her fourth-grade students’ learning. But many could not complete it. Only three of the 20 students in her homeroom have sufficient internet access at home. The rest do not have service or can use only their parents’ cellphones.

A few miles away in Fort Towson, Okla., which has about 600 residents, Mayor Tami Barnes said people complained constantly about internet speeds, which she called a “huge damper” on the local economy. On a recent afternoon, the busiest part of town was the parking lot of a convenience store and gas station. The other two main businesses are a steakhouse and Dollar General store.

Although internet bills are a financial burden for many families, Ms. Barnes said more residents would probably attend medical appointments online if they had high-speed access, because many often travel up to three hours to see specialized doctors.

Other states with low population densities, such as Montana, could also face more challenges. In Broadwater County, Mont., where many homes are separated by vast stretches of grassy land and some are tucked in mountainous areas, residents said the lack of fast service made it difficult to do things like work from home.

Denise Thompson, 58, who operates a cattle ranch with her husband in Townsend, Mont., said she wanted to start a website to ship more beef products, but she was unsure how she could operate it at home because she relied on her phone’s hot spot for internet access and her connection was slow. She has not tried streaming a movie in about a year because it is usually stuck buffering for minutes.

Her house sits in a gulch in between two tall hills and her nearest neighbor is about three miles away, so her only other option is satellite service. Even with the new federal money, Ms. Thompson said she was skeptical she would see more reliable options.

“I really don’t expect that to happen,” she said.

Lindsey Richtmyer, a county commissioner, said many locations would be categorized as underserved but actually received slower service than reflected by the F.C.C.’s map. County officials are encouraging residents to take state speed tests in hopes of identifying much of the area as unserved.

Estimates have found that Montana would need more than $1.2 billion to deploy fiber to all unserved and underserved locations, a shortfall of more than $500 million. Misty Ann Giles, the director of Montana’s Department of Administration, said a mix of technologies would be required to reach everyone, because deploying fiber could cost the state up to $300,000 in some locations.

“Obviously more money would have been appreciated,” she said. “But we’re going to figure it out and make it work.”