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Despite the mission’s fiery outcome, Bill Nelson, the NASA administrator, offered congratulations to the company. “Every great achievement throughout history has demanded some level of calculated risk, because with great risk comes great reward,” Mr. Nelson wrote on Twitter.

The space agency is relying on SpaceX to build a version of Starship that will carry two astronauts from lunar orbit to the surface of the moon during its Artemis III mission. There was great anticipation from the flight, which had been delayed from Monday as the gargantuan rocket could one day carry massive amounts of cargo and many people into space.

Before the launch, which had no people aboard and aimed to validate whether the design of the rocket system is sound, Elon Musk, the company’s founder, had tamped down expectations. He said it might take several tries before Starship succeeds at this test flight.

But the launch achieved a number of important milestones, with the rocket flying for four minutes and getting well clear of the launchpad. The brief flight produced reams of data for engineers to understand how the vehicle performed.

“It may look that way to some people, but it’s not a failure,” said Daniel Dumbacher, executive director of the American Institute of Aeronautics and Astronautics and a former high-level NASA official. “It’s a learning experience.”

Still, the flight fell short of complete success. The flight plan called for the Starship spacecraft to reach a higher altitude of about 150 miles before splashing down in the Pacific Ocean near Hawaii about 90 minutes later. And it remains to be seen how Thursday’s flight outcome might affect NASA’s schedule, which optimistically calls for the first moon landing by astronauts aboard Starship to occur in late 2025.

When SpaceX began building Starship, it was motivated by Mr. Musk’s dream of sending people to live on Mars someday, an endeavor that would require the transport of enormous amounts of supplies to succeed.

But entrepreneurs and futurists are thinking closer to home. A gargantuan, fully reusable vehicle would slash the cost of sending things to space, leading some to imagine how Starship could carry mammoth space telescopes to peer at the cosmos, or squadrons of robots to explore other worlds. Others are designing larger satellites that will be cheaper because they will not have to use expensive components currently needed to fit into the size and weight constraints imposed by present-day rockets.

“Flying rockets and reusing them has massive potential to change the game and transportation to orbit,” said Phil Larson, who served as a White House space adviser during the Obama administration and later worked on communication efforts at SpaceX. “And it could enable whole new classes of missions.”

Despite the setback, SpaceX remains the dominant company in global spaceflight. Its rockets have already traveled to space 25 times in 2023, with the most recent launch concluding successfully on Wednesday.

The countdown on Thursday at the launch site in South Texas, near the city of Brownsville, proceeded smoothly through the morning until the last half a minute, when it was paused for a few minutes while SpaceX engineers resolved technical issues. Employees at SpaceX headquarters in California started cheering loudly when the countdown resumed.

Then as a cloud of exhaust rose around the rocket, it took flight.

“It looked really good coming off the pad, and it looked really good for a while,” Mr. Dumbacher said.

In an update, SpaceX said the rocket got as high as about 24 miles over the Gulf of Mexico. Video of the rocket captured flashes as several of the 33 engines failed on the lower portion of the spacecraft, the Super Heavy booster. That turned out to be too much for the guidance system to compensate, and the vehicle started tumbling in a corkscrew path.

“This does not appear to be a nominal situation,” John Insprucker, a SpaceX engineer, reported during the company’s livestream of the launch.

The upper-stage Starship vehicle apparently did not separate from the booster, and four minutes after liftoff, the automated flight termination system destroyed the rocket, ending the flight in a fireball.

The launch lived up to SpaceX’s promise of “excitement guaranteed.” And it avoided a worst-case outcome of exploding on the launchpad, which would have required extensive repairs.

Mr. Musk offered congratulations to the SpaceX team on Twitter. “Learned a lot for next test launch in a few months,” he said.

Karl Kriegh, 69, and his wife traveled from Colorado for the launch, and lingered afterward on the beach at South Padre Island, where viewers were taking in the flight from a safe distance.

“I’m so glad I’ve lived to see this,” he said. “It was incredibly dramatic, one of those things on the bucket list.”

Carlos Huertas, 42, a stage tech who lives in Los Angeles, was on the beach wearing a T-shirt sold by SpaceX that said “Occupy Mars.”

“I thought it turned out well until I learned it exploded,” he said. He added that he felt “a little disappointed even though we knew it was a big possibility” and said he hoped to see another launch soon.

Heavy-lift rockets like Starship are inherently more complex and more difficult to develop than smaller rockets, just as building an aircraft carrier takes much more work than a modest yacht. In addition, by aiming to make all pieces of the spacecraft reusable and capable of launching again a few hours after landing, SpaceX is attempting an engineering challenge that goes beyond what was accomplished in the previous 60 years of the space age.

It is not a surprise to experts that SpaceX did not fully succeed on the first try.

“They might have a couple of questions to go look at in terms of why some of the engines may not have been running,” Mr. Dumbacher said. “They’ll look into it, they’ll figure it out, and they’ll come back the next time and they’ll fix those problems and they’ll move on to the next one end eventually they’ll get this flying all the way in orbit. I’m fully confident of that.”

However, SpaceX has a history of learning from mistakes. The company’s mantra is essentially, “Fail fast, but learn faster.”

Traditional aerospace companies have tried to anticipate and prevent as many failures as possible ahead of time. But that approach takes money and time and can lead to vehicles that are overdesigned. SpaceX instead is more like a Silicon Valley software company — starting with an imperfect product that can be improved quickly.

When it tried to start landing Falcon 9 boosters, the first few hit too hard and exploded. With each attempt, SpaceX engineers tweaked the systems. After its first successful landing, more soon followed. Today, it is a rare surprise if a booster landing fails.

A couple of years ago, the company took a similar approach to fine-tuning the landing procedure for Starship. In a series of tests, prototypes of Starship lifted off to an altitude of about six miles before shutting off its engines. It then belly flopped through the atmosphere to slow its rate of fall before tilting back to vertical and firing its engines again for landing. The first few ended explosively before one attempt finally succeeded.

SpaceX, as one of the most valuable privately held companies, possesses a large financial cushion to absorb setbacks, unlike its early days when the first three launches of its original rocket, the small Falcon 1, failed to reach orbit. Mr. Musk scraped together just enough money and parts for a fourth launch attempt. Had it failed, SpaceX would have gone out of business. The fourth Falcon 1 launch succeeded, and SpaceX has succeeded in almost all of its endeavors since, even when it sometimes fails at first.

Big NASA programs like the Space Launch System, which NASA used on an uncrewed mission to the moon in November, are generally not afforded the same luxury of explode-as-you-learn.

“Government programs are not allowed to operate that way because of that, because of the way we have all the stakeholders being able to watch over and tell you no,” Mr. Dumbacher said.

Back on the beach, people who turned up for the launch took the day’s outcome in stride.

“Would it have been awesome if it didn’t explode?” said Lauren Posey, 34. “Yeah. But it was still awesome.”

James Dobbins contributed reporting from South Padre Island, Texas.