Yet while Mr. Bridges had no work history, he had certain skills. He had built and sold some stripped-down personal computers, and he had studied information technology at a community college. When Mr. Bridges heard IBM was hiring at a nearby operations center in 2013, he applied and demonstrated those skills.

Now Mr. Bridges, 25, is a computer security analyst, making $45,000 a year. In a struggling Appalachian economy, that is enough to provide him with his own apartment, a car, spending money — and career ambitions.

“I got one big break,” he said. “That’s what I needed.”

Mr. Bridges represents a new but promising category in the American labor market: people working in so-called new-collar or middle-skill jobs. As the United States struggles with how to match good jobs to the two-thirds of adults who do not have a four-year college degree, his experience shows how a worker’s skills can be emphasized over traditional hiring filters like college degrees, work history and personal references. And elevating skills over pedigree creates new pathways to employment and tailored training and a gateway to the middle class.

This skills-based jobs approach matters at a time when there is a push to improve the circumstances of those left behind in the American economy, many of whom voted for President Trump.

“We desperately need to revive a second route to the middle class for people without four-year college degrees, as manufacturing once was,” said Robert Reich, a labor secretary in the Clinton administration who is now a professor at the University of California, Berkeley. “We have to move toward a system that works.”

The skills-based concept is gaining momentum, with nonprofit organizations, schools, state governments and companies, typically in partnerships, beginning to roll out such efforts. On Wednesday, the approach received a strong corporate endorsement from Microsoft, which announced a grant of more than $25 million to help Skillful, a program to foster skills-oriented hiring, training and education. The initiative, led by the Markle Foundation, began last year in Colorado, and Microsoft’s grant will be used to expand it there and move it into other states.

“We need new approaches, or we’re going to leave more and more people behind in our economy,” said Brad Smith, president of Microsoft.

It is unclear whether a relative handful of skills-centered initiatives can train large numbers of people and alter hiring practices broadly. But the skills-based approach has already yielded some early and encouraging results in the technology industry, which may provide a model for other industries.

These jobs have taken off in tech for two main reasons. For one, computing skills tend to be well defined. Writing code, for example, is a specific task, and success or failure can be tested and measured. At the same time, the demand for tech skills is surging.

One tech project that has expanded rapidly is TechHire, which was created in 2015 and is the flagship program of Opportunity@Work, a nonprofit social enterprise. TechHire provides grants and expertise to train workers around the country and link them to jobs by nurturing local networks of job seekers, trainers and companies.

In just two years, TechHire’s network has grown to 72 communities, 237 training organizations and 1,300 employers. It has helped place more than 4,000 workers in jobs.

TechHire’s mission is partly to chip away at “the cultural hegemony of the bachelor’s degree,” said Byron Auguste, president of Opportunity@Work.

Nichole Clark of Paintsville, Ky., heard a radio ad last year for TechHire Eastern Kentucky. The program offered six months of training in software programming that included working with a company while being paid $400 a week. That was not much less than what Ms. Clark, now 24, was making as a manager at Pizza Hut.

Without a college degree, Ms. Clark said, her horizons seemed confined to low-wage jobs in fast-food restaurants, retail stores or doctors’ offices. The TechHire program, she said, could be “a doorway to a good-paying job, which is everything here.”

Ms. Clark made it through online screening tests and an interview and got into the program. TechHire’s role varies, and it often funds training grants, but in this program it solicited applicants and advised and shared best practices with Interapt, a software development and consulting company. The training stipends were paid for with a $2.7 million grant from the Appalachian Regional Commission.

After four months of taking all-day classes on the basics of writing software and two months of working in an internship alongside Interapt developers, Ms. Clark was hired by Interapt in May. As a member of the team that performs software quality assurance and testing, she is now paid more than $40,000 a year, about double what she made at Pizza Hut.

Ms. Clark is growing confident about her employment future. “There are endless roles you can play, if you have these skills,” she said.

In Colorado, Skillful is working to improve the flow of useful information among job seekers, employers, educators, governments and local training groups. The organization focuses on jobs in tech, health care and advanced manufacturing.

Ninety companies have worked with Skillful’s staff and partners to refine and clarify their descriptions of skills. That data has contributed to an online “training finder” tool — built by researchers at LinkedIn — that shows salary ranges, skills required, training programs and nearby openings for different occupations. (Microsoft acquired LinkedIn, a Skillful partner, last year.)

“We’re trying to use the very forces that are disrupting the economy — technology and data — to drive a labor market that helps all Americans,” said Zoë Baird, chief executive of the Markle Foundation.

Ron Gallegos Jr., 31, has benefited from Skillful’s program. For years, he worked as a facilities manager overseeing cleaning crews in retail locations. Restless, he wanted to pursue a tech career.

He had a side gig fixing televisions, gadgets and PCs. But he was self-taught, had no college degree and needed training and credentials.

So in late 2015, Mr. Gallegos quit his job to study full time to gain training and certifications as a computer support technician, and later in network security.

At his local community college, Skillful representatives offered tips on job searches, résumé preparation, financial support and networking. At one event, Mr. Gallegos learned of a state grant available for a security course he wanted to take.

The program’s career coaches also emphasized the so-called soft skills of speaking concisely, working cooperatively and attending industry and professional gatherings to meet people, Mr. Gallegos said.

Not content to just look for jobs, Mr. Gallegos created one for himself, setting up Mile High IT Services last fall. Now he works as a technology-support contractor for small businesses, and his one-man company is gaining traction, with his income exceeding $50,000 a year.

“It’s all pretty bright for me now,” he said.

In Rocket Center, where rocket engines were once built and some composite materials for American fighter jets are manufactured today, IBM occupies a few buildings and employs 350 people, including Mr. Bridges. They are working on cloud computing, cybersecurity, application development and help desks.

In the last two years, nearly a third of IBM’s new hires there and in a few other locations have not had four-year college degrees. IBM has jointly developed curriculums with the local community college, as well as one-year and two-year courses aligned with the company’s hiring needs.

For companies like IBM, which has 5,000 job openings in the United States, new-collar workers can help it meet its work force needs — and do it inexpensively if those workers are far away from urban centers, where the cost of living and prevailing wages are higher.

“It makes sense for our business, for the job candidates and for the communities,” said Sam Ladah, IBM’s vice president for talent.

The company, which stopped disclosing its American employment in 2007 and regularly cuts jobs in declining businesses, declined to say whether it was increasing its total domestic work force.

But at the West Virginia center, IBM plans to hire up to 250 people this year, including more like Mr. Bridges.

“Now, we’re recruiting for skills,” Mr. Ladah said.