When Suki Lanh was laid off from a fintech insurance startup in early July, she worried it could take months to find a new job.

“I was definitely nervous seeing the amount of startups that were laying off folks,” the 30-year-old said. “I just thought generally it was going to be really difficult to get another job for a while.”

Ms. Lanh posted a video about her job loss on LinkedIn two days after she was let go amid broader cuts at a New York City-based startup. Recruiter messages started flooding her inbox.

“I was honestly surprised at how many places were hiring or looking for someone,” she said.

Within 2½ weeks, the Tampa, Fla., resident had advanced to final-stage interviews with seven companies and scored job offers from two of them. She accepted a remote copywriting job at Walgreens in late July with a salary about 50% higher than in her previous job. Ms. Lanh is looking forward to adding a modern, humorous flair to product advertisements for the pharmacy-store chain.

Jobless claims, percentage change since January 2022

Companies in a broadening array of industries are announcing layoffs as they struggle with declining business activity, rising interest rates, high inflation and shifting consumer-spending habits.

Ford Motor Co. confirmed Monday it is laying off roughly 3,000 white-collar and contract employees, and furniture company Wayfair Inc. recently said it was laying off 5% of its global workforce.

But one characteristic of today’s economy is that job cuts at small startups and large companies have yet to dent the overall labor market. Labor demand is still historically strong, offering only faint signs of cooling. There are nearly two job openings for every unemployed person seeking work. That means many workers who are losing their jobs are quickly landing jobs. Some are even weighing multiple offers and accepting positions that pay more and better align with their skills.

“With unemployment so low, job openings so high and the quits rate so high, we’re finding that the balance of power is still with the job seeker,” said Paul McDonald, senior executive director at staffing firm Robert Half.

Initial jobless claims, the number of applications for state unemployment benefits, have risen this summer after hitting a half-century low in the spring. In the week ended Aug. 13, a seasonally adjusted 250,000 workers filed for benefits, above the 2019 prepandemic average of 218,000 and a sign that layoffs have ticked up.

Meanwhile, continuing claims, a proxy for the number of people claiming ongoing jobless benefits, have increased at a much slower rate. Continuing claims were about 1.4 million in the week ended Aug. 6, below their 2019 average of 1.7 million. Relatively low and stable continuing claims could indicate workers are leaving unemployment rolls quickly as they regain employment, some economists say.

Reggie Pearson, of Columbia, S.C., said he found out in a morning Zoom call earlier this month that he was losing his management job as part of broader layoffs at a health-insurance broker. Though he had been discussing a new job opportunity for several weeks with insurance company Baldwin Risk Partners, nothing was concrete. The 42-year-old thought it could take a month to secure a new job.

Around 1 p.m. ET that same day, a recruiter for Baldwin Risk called Mr. Pearson with a job offer in sales management. The recruiter told Mr. Pearson that this was the first time he had made a job offer to someone the same day they had also gotten laid off.

“I went from being lost and confused to being happy and excited and like, ‘man, this is a blessing,’” Mr. Pearson said.

By 2 p.m., he had received an offer letter, with an annual salary of $115,000, well above his previous pay of $60,000, he said. He signed it immediately. Mr. Pearson said he is excited to share his energy—powered by morning runs and lots of water—with colleagues in his new Charlotte, N.C., workplace. He also is helping recruit roughly 20 to 30 sales agents by October for the division he oversees.

The typical unemployed worker had been off the job for 8.5 weeks in July, down from 14.4 weeks a year earlier, according to the Labor Department. The shorter duration of unemployment suggests many unemployed Americans are finding jobs fast as fewer leave the labor force, said Julia Pollak, chief economist at ZipRecruiter.

Shorter episodes of joblessness defy economists’ concerns earlier in the pandemic that workers would suffer from long-term spells of unemployment of 27 weeks or more like they did after the 2007-09 recession.

The share of all jobless Americans unemployed for less than five weeks surpassed the share of those out of work for at least 27 weeks in January, according to the Labor Department. The gap has since widened. By July, nearly 37% of unemployed workers had been out of work less than five weeks, roughly double the percentage experiencing long-term joblessness.