Two months ago, Kyle Vogt, the chief executive of Cruise, choked up as he recounted how a driver killed a 4-year-old girl in a stroller at a San Francisco intersection. “It barely made the news,” he said, pausing to collect himself. “Sorry. I get emotional.”

To make streets safer, he said in an interview, cities should embrace self-driving cars like those designed by Cruise, a subsidiary of General Motors. They do not get distracted, drowsy or drunk, he said, and being programmed to put safety first meant they could substantially reduce car-related fatalities.

Now Mr. Vogt’s driverless car company faces its own safety concerns as he contends with angry regulators, anxious employees and skepticism about his management and the viability of a business that he has often said will save lives while generating billions of dollars.

On Oct. 2, a car hit a woman in a San Francisco intersection and flung her into the path of one of Cruise’s driverless taxis. The Cruise car ran over her, briefly stopped, and then dragged her some 20 feet before pulling to the curb, causing severe injuries.

California’s Department of Motor Vehicles last week accused Cruise of omitting the woman being dragged from a video of the incident it initially provided to the agency. The D.M.V. said the company had “misrepresented” its technology and told Cruise to shut down its driverless car operations in the state.

Two days later, Cruise went further and voluntarily suspended all of its driverless operations around the country, taking 400 or so driverless cars off the road. Since then, Cruise’s board has hired the law firm Quinn Emanuel to investigate the company’s response to the incident, including its interactions with regulators, law enforcement and the media.

The board plans to evaluate the findings and any recommended changes. Exponent, a consulting firm that evaluates complex software systems, is conducting a separate review of the crash, said two people who attended a companywide meeting at Cruise on Monday.

Cruise employees worry that there is no easy way to fix the company’s problems, said five former and current employees and business partners, while its rivals fear Cruise’s issues could lead to tougher driverless car rules for all of them.

Company insiders are putting the blame for what went wrong on a tech industry culture — led by the 38-year-old Mr. Vogt — that prioritized speed over safety. In the competition between Cruise and its top driverless car rival, Waymo, Mr. Vogt wanted to dominate in the same way Uber dominated its smaller ride-hailing competitor, Lyft.

“Kyle is a guy who is willing to take risks and he is willing to move quickly. He is very Silicon Valley,” said Matthew Wansley, a professor at the Cardozo School of Law in New York who specializes in emerging automotive technologies. “That both explains the success of Cruise and its mistakes.”

When Mr. Vogt spoke to the company about its suspended operations on Monday, he said he did not know when they could start again and that layoffs could be coming, according to two employees who attended the companywide meeting.

He acknowledged that Cruise had lost the public’s trust, the employees said, and outlined a plan to win it back by being more transparent and putting more emphasis on safety. He named Louise Zhang, vice president of safety, as the company’s interim chief safety officer and said that she would report directly to him.

“Trust is one of those things that takes a long time to build and just seconds to lose,” Mr. Vogt said., according to attendees. “We need to get to the bottom of this and start rebuilding that trust.”

Cruise declined to make Mr. Vogt available for an interview. G.M. said in a statement that its “commitment to Cruise with the goal of commercialization remains steadfast.” It said that it believed in the company’s mission and technology and supported its steps to put safety first.

Mr. Vogt began working on self-driving cars as a teenager. When he was 13, he programmed a Power Wheels ride-on toy car to follow the yellow line in a parking lot. He later participated in a government-sponsored self-driving car competition while studying at the Massachusetts Institute of Technology.

In 2013, he started Cruise Automation. The company retrofitted conventional cars with sensors and computers to operate autonomously on highways. He sold the business three years later to G.M. for $1 billion.

After the deal closed, Dan Ammann, G.M.’s president, took over as Cruise’s chief executive and Mr. Vogt became its president and chief technology officer.

As president, Mr. Vogt built out Cruise’s engineering team while the company expanded to about 2,000 employees from 40, former employees said. He championed bringing cars to as many markets as fast as possible, believing that the speedier the company moved, the more lives it would save, former employees said.

In 2021, Mr. Vogt took over as chief executive. Mary T. Barra, G.M.’s chief executive, began including Mr. Vogt on earnings calls and presentations, where he hyped the self-driving market and predicted that Cruise would have one million cars by 2030.

Mr. Vogt pressed his company to continue its aggressive expansion, learning from problems its cars ran into while driving in San Francisco. The company charged an average of $10.50 per ride in the city.

After a Cruise vehicle collided with a Toyota Prius driving in a bus lane last summer, some people at the company proposed having its vehicles temporarily avoid streets with bus lanes, former employees said. But Mr. Vogt vetoed that idea, saying Cruise’s vehicles needed to continue to drive those streets to master their complexity. The company later changed its software to reduce the risk of similar accidents.

In August, a Cruise driverless car collided with a San Francisco fire truck that was responding to an emergency. The company later changed the way its cars detects sirens.

But after the crash, city officials and activists pressured the state to slow Cruise’s expansion. They also called on Cruise to provide more data than details about collisions, including documentation of unplanned stops, traffic violations and vehicle performance, said Aaron Peskin, president of San Francisco’s Board of Supervisors.

“Cruise’s corporate behavior over time has increasingly led to a lack of trust,” Mr. Peskin said.

With its business frozen, there are concerns that Cruise is becoming too much of a financial burden on G.M. and is hurting the auto giant’s reputation. Ms. Barra told investors that Cruise had “tremendous opportunity to grow” just hours before California’s D.MV. told Cruise to shut down its driverless operations.

Cruise has not collected fares or ferried riders in more than a week. In San Francisco, Phoenix, Dallas, Houston, Miami, and Austin, Texas, hundreds of Cruise’s white and orange Chevrolet Bolts sit stagnant. The shutdown complicates Cruise’s ambition of hitting its goal of $1 billion of revenue in 2025.

G.M. has spent an average of $588 million a quarter on Cruise over the past year, a 42 percent increase from a year ago. Each Chevrolet Bolt that Cruise operates costs $150,000 to $200,000, according to a person familiar with its operations.

Half of Cruise’s 400 cars were in San Francisco when the driverless operations were stopped. Those vehicles were supported by a vast operations staff, with 1.5 workers per vehicle. The workers intervened to assist the company’s vehicles every 2.5 to 5 miles, according to two people familiar with is operations. In other words, they frequently had to do something to remotely control a car after receiving a cellular signal that it was having problems.

To cover its spiraling costs, G.M. will need to inject or raise more funds for the business, said Chris McNally, a financial analyst at Evercore ISI. During a call with analysts in late October, Ms. Barra said that G.M. would share its funding plans before the end of the year.