It’s not yet the same as hopping on commuter flight from New York to Washington or renting a car from Avis, but Sunday’s launch of four astronauts to the International Space Station in a capsule built by SpaceX was a momentous step toward making space travel commonplace and mundane.

In the future, instead of relying on government-operated spacecraft, NASA astronauts and anyone else with enough money can buy a ticket on a commercial rocket.

“This is truly a commercial launch vehicle,” Jim Bridenstine, the NASA administrator, said during a post-launch news conference, “and we’re grateful to our partners at SpaceX for providing it.”

NASA designated Sunday night’s launch as the first operational flight of the Crew Dragon spacecraft built and operated by SpaceX, the rocket company started by Elon Musk. The four astronauts aboard — three from NASA, one from JAXA, the Japanese space agency — left Earth from the Kennedy Space Center in Florida.

A Crew Dragon took two astronauts — Robert Behnken and Douglas Hurley — to the space station in May, but that was a test flight to shake out remaining glitches in the systems.

The four astronauts on this flight are Michael S. Hopkins, Shannon Walker and Victor J. Glover of NASA and Soichi Noguchi, a Japanese astronaut.

NASA and SpaceX last week completed the certification process, which provides the space agency’s seal of approval that SpaceX has met the specifications set out for regularly taking NASA astronauts to orbit. This launch, known as Crew-1, is a regularly scheduled trip to take four crew members for a six-month stay at the space station.

“It marks the end of the development phase of the system,” Phil McAlister, director of commercial spaceflight development at NASA, said in a telephone interview with reporters on Thursday. “For the first time in history, there is a commercial capability from a private sector entity to safely and reliably transport people to space.”

Despite iffy weather — forecasts gave only a 50-50 chance of favorable conditions at the launchpad — the skies remained clear enough. At 7:27 p.m. Eastern time, the nine engines of the Falcon 9 rocket roared to life and brightened the night sky as the rocket arced over the Atlantic Ocean.

After dropping away from the second stage, which continued to orbit, the Falcon 9 booster turned around and landed on a floating platform. SpaceX now, as a matter of course, recovers and reuses the boosters. This same rocket stage will be used to launch the next quartet of astronauts to the space station next spring.

The Crew Dragon, named Resilience, is scheduled to dock on Monday at about 11 p.m. after a 27.5 hour trip as the capsule caught up with space station, which is traveling at more than 17,000 miles per hour.

When Mr. Glover arrives, he will become the first Black astronaut to serve as a member of the station’s crew in the 20-some years that people have been living aboard the International Space Station. Other Black astronauts have previously been aboard the space station, but they were there for briefer stays during space shuttle missions that helped assemble the orbiting outpost.

When asked during a news conference on Monday about his thoughts on making history, Mr. Glover modestly nodded to the significance.

“It is something to be celebrated once we accomplish it, and I am honored to be in this position and to be a part of this great and experienced crew,” he said. “And I look forward to getting up there and doing my best to make sure, you know, we are worthy of all the work that’s been put into setting us up for this mission. You know, unlike the election — that is in the past or receding in the past — this mission is still ahead of me. So, let’s get there, and I’ll talk to you after I get on board.”

He also said last week in an interview with The Christian Chronicle, a publication of the Churches of Christ, that the milestone was “bittersweet.”

“I’ve had some amazing colleagues before me that really could have done it, and there are some amazing folks that will go behind me,” Mr. Glover said. “I wish it would have already been done, but I try not to draw too much attention to it.”

Charles F. Bolden Jr., who served as NASA administrator under President Barack Obama, said that while Mr. Glover was making history, he should not feel burdened.

“Several of us have had an opportunity to try to talk with him regularly and try to help put him at ease and help him understand he’s not carrying the weight of the world on his shoulders,” said Mr. Bolden, who is also Black and spent almost 700 hours in space as a NASA astronaut. “He shouldn’t feel unusual responsibility because he’s Black. He should just go and be another crew member and have a good time.”

On Sunday afternoon, as the astronauts prepared for the launch, they were visited by Mr. Bridenstine and Gwynne Shotwell, the president and chief operating officer of SpaceX.

For Mr. Bridenstine, this was the last astronaut launch he would view as leader of NASA. In an interview last week with the magazine Aviation Week, Mr. Bridenstine said he would not, even if asked by the incoming Biden administration, stay on in his current role past the Jan. 20 inauguration.

Mr. Musk, the chief executive of SpaceX, remained out of sight after he said he “most likely” had a “moderate case” of Covid-19.

At the space station, the four astronauts who lifted off on Sunday will join three others already there: Kate Rubins of NASA and two Russians, Sergey Ryzhikov and Sergey Kud-Sverchkov.

They will be doing what astronauts have been doing for the past two decades on the space station: overseeing scientific experiments, performing maintenance tasks, talking to students on the ground.

The astronauts, for example, will be collecting their own biological samples to help scientists on the ground study how dietary changes affect the body. The astronauts will also be growing radishes, the latest experiment to explore whether food can be grown in space. (Red lettuce and mizuna mustard greens are among earlier foods that the astronauts have studied.) They will also test whether fungi can break apart asteroid rock and help extract useful metals — a scientific prelude to extraterrestrial mining operations, and a follow-up to a similar, successful experiment that used bacteria.

With Crew Dragon entering operational status, the crew of the space station can be increased to seven. Since the retirement of the space shuttles, the Russian Soyuz spacecraft was the only means for astronauts traveling to and from the space station. The Soyuz only has three seats, and they also serve as lifeboats in case of an emergency there — with two Soyuzes docked there, the maximum size of the crew was six.

But for now, there are not places for seven astronauts to sleep there. “We are currently short one crew quarters on board station,” Mr. Hopkins said during a news conference on Monday. “There are plans to to have a temporary station that will be up there. Not sure when it’s going to arrive. It could arrive mid mission, or it may not get up there while we’re still on board.”

Mr. Hopkins, the commander of the SpaceX crew, said that he might sleep in the Crew Dragon instead.

During the post-launch news conference, Ms. Shotwell said SpaceX would be launching about seven Dragon missions, some to launch astronauts, some to carry cargo, during the next 15 months. Those would almost all be for NASA, she said, but it was possible that it could include one for a private customer.

A couple of companies have announced that they are buying flights on the Crew Dragon to take wealthy private citizens for out-of-this-world vacations. One company, Axiom Space, will take three tourists to the space station, perhaps as soon as late 2021.

One passenger could be the actor Tom Cruise. Mr. Bridenstine confirmed in May that NASA was working with Mr. Cruise to help make a movie at the space station.

Michael T. Suffredini, the president and chief executive of Axiom Space, would not confirm whether Mr. Cruise was booked on the Axiom flight, saying the company does not disclose information about its customers.

Last week, Axiom said all three available seats had been sold. The fourth seat would be filled by an Axiom employee, Michael López-Alegría, a former NASA astronaut.

The other company, Space Adventures, is offering a free-flying Crew Dragon flight that will not dock at the space station, but instead will go around Earth on a highly elliptical orbit that will provide passengers with a view of the planet from a very high perch.

Mr. Bridenstine, in remarks concluding the Sunday night news conference, repeated what he has said many times before, that a new era is opening for NASA and the space industry.

“We are now going into basically operational missions that are commercial in nature, where NASA is a customer.” he said, “Our goal has been and will be to be one customer of many customers in a very commercial marketplace in low-Earth orbit.”

Katherine J. Wu contributed reporting.