By late last week, President Trump had decided to fire Gen. Charles Q. Brown Jr., the chairman of the Joint Chiefs of Staff, and replace him with one of two very different candidates, according to two administration officials.

One was Gen. Michael E. Kurilla, a hard-charging Army four-star general who oversees U.S. military operations in the Middle East, one of the Pentagon’s highest-profile assignments.

The other was a little-known retired three-star Air Force officer, Dan Caine, with an unorthodox career path that included time as a fighter pilot, the top military liaison to the C.I.A. and an Air National Guard officer who founded a regional airline in Texas.

Mr. Trump and General Caine met for an hour at the White House on Feb. 14. The president largely made up his mind during a meeting with Defense Secretary Pete Hegseth on Thursday, aides said.

And in a message on social media the next evening, Mr. Trump announced that he had picked General Caine, calling him “an accomplished pilot, national security expert, successful entrepreneur, and a ‘warfighter’ with significant interagency and special operations experience.”