It was a bold move for a general recently nominated for promotion by Mr. Trump, who at the time was furious about what he viewed as Pentagon intransigence over his desire to deploy active duty troops to city streets to take on racial justice protesters.

But General Brown was unanimously confirmed by the Senate, and Time magazine named him one of the most influential people of 2020 months later.

General Brown, who declined to speak for this article, as did General Berger, has spoken about inclusion on other occasions. In an Air Force recruiting ad that aired during the pregame show for the N.B.A. finals in 2021, he came off as a take-no-prisoners fighter pilot: “When I’m flying, I put my helmet on, my visor down, my mask up,” he said, staring into the camera, to interspersing footage that could be straight out of “Top Gun,” if the movie franchise was about Air Force and not Navy pilots. “You don’t know who I am, whether I’m African American, Asian American, Hispanic, white, male or female.”

“You just know I’m an American airman, kicking your butt. I’m General C.Q. Brown Jr. Come join us.”

The commercial received widespread praise on social media.

General Brown was once questioned for parking his car in the designated spot for the Pacific Air Forces commander, back when he actually was the Pacific Air Forces commander.

He has evinced humility — he told a National Press Club audience that he would give himself a “C” for putting change in place in the giant institution he commands. But he also has swagger — he irritated his bosses last summer when he said at the Aspen Security Forum that the United States might provide fighter jets to Ukraine and train its pilots how to fly them. The Biden administration may yet end up doing this, but the White House was not ready to make any such announcement last year.

Since then, General Brown has gone back to being cautious. Until, his friends say, he decides, again, not to be.