Just four days after being named the next White House chief of staff, Susie Wiles was waiting patiently for an espresso drink at a five-star hotel in Las Vegas.

Overnight, she had become one of the most powerful people in America. The value of a minute of her time could not be higher during the presidential transition: Republican strivers are hounding her for desirable gigs, and back at Mar-a-Lago, President-elect Donald J. Trump has kept courting controversy with his picks.

Yet here she was thousands of miles away, flanked only by a security guard, alone in line at a Four Seasons coffee shop. She had just peeled off from lunch with other top Trump campaign officials, including her fellow campaign manager, Chris LaCivita; the pollster Tony Fabrizio; and the campaign’s fund-raising chief, Meredith O’Rourke. “We’re all just chilling,” one member of the startled Trump entourage joked aloud when alerted that they had been spotted by a nearby New York Times reporter as they walked through the hotel.

What demanded the dayslong presence of all these Trumpworld figures during some of the most important weeks of their careers? The fall gathering of a secretive group of wealthy tech executives and their allies who have ascended swiftly within the Republican Party’s donor class: the Rockbridge Network.

The group, which was co-founded five years ago by JD Vance, sprouted from an informal set of dinners into a powerful coalition of Republican donors who have given more than $100 million to Rockbridge projects since 2019, according to a person close to the group, helping lead Silicon Valley’s march to the right. For Rockbridge, Mr. Vance’s election as vice president was a crowning achievement — and a tantalizing opportunity to wield new national influence.

But Rockbridge has largely kept its activities stealthy, mindful of how groups of wealthy conservatives like the Koch Network have drawn attacks from both liberal detractors and Republican wannabes.