On Thursday morning, at a time when most people in the United States were sleeping, Jeff Bezos’ space company sent its first rocket into orbit.

At 2:03 a.m. Eastern time, seven powerful engines ignited at the base of a 320-foot-tall rocket named New Glenn. The flames illuminated night into day at Cape Canaveral Space Force Station in Florida. The rocket, barely moving at first, nudged upward and then accelerated in an arc over the Atlantic Ocean, lit up in blue, the color of combustion of the rocket’s methane fuel.

Thirteen minutes later, the second stage of New Glenn reached orbit.

The launch was a major success for Blue Origin, Mr. Bezos’ rocket company. It should quiet critics who say that the company has been too slow compared with Elon Musk’s SpaceX, which has dominated global spaceflight industry in recent years. New Glenn could prove a credible competitor with Mr. Musk’s company and win launch contracts from NASA and the Department of Defense, as well as commercial contracts.

For at least one moment, however, the two richest people in the world warmly cheered each other.

“Congratulations on reaching orbit on the first attempt!” Mr. Musk wrote on X, the social media site that he owns.

“Thank you!” Mr. Bezos replied.

Mr. Bezos posted a series of pictures and videos. “Beautiful,” Mr. Musk commented on one of the images.