Mr. Ito dropped out of Tufts University and the University of Chicago, ran a Tokyo nightclub called XY Relax and led a series of internet companies — as well as a guild in World of Warcraft, the online role-playing game. He had an eye for good ideas, investing early on in Twitter, Kickstarter and Flickr, but it was his mastery of cultivating relationships that was especially valuable to the lab.

Reid Hoffman, a founder of LinkedIn, once said Mr. Ito “makes well-networked professionals look like hermits.” His mentors include Lawrence Lessig, the influential law professor and founder of Creative Commons, the nonprofit advocate for public intellectual property rights, where Mr. Ito was once chief executive. His online photo albums include pictures of the cellist Yo-Yo Ma, the astronaut Leland Melvin and the filmmaker J. J. Abrams, a “director’s fellow” at the lab. And when Mohammed bin Salman, the crown prince of Saudi Arabia, toured the United States last year — before the death of the Washington Post journalist Jamal Khashoggi — he attended a reception at the Media Lab.

It was perhaps inevitable that Mr. Ito would meet Mr. Epstein, another prolific networker. Both men attended the 1999 Billionaires’ Dinner, an annual event put on by the literary agent John Brockman, and belonged to the invitation-only Trilateral Commission in 2003.

At Wednesday’s meeting, Mr. Ito said he had met Mr. Epstein in a hotel lobby during a conference in 2013, five years after Mr. Epstein’s plea in Florida. Mr. Epstein long cultivated relationships with celebrity scientists, many of whom Mr. Ito also knew, and eagerly associated himself with the Media Lab. In 2014, he issued news releases about donations to restore Mark Rothko murals on the campus and teach coding to 5-year-olds. (The Media Lab later called those statements inaccurate.)

The lab served as an avenue for Mr. Epstein to seek connections to the wider tech world.

Elizabeth Stark, the chief executive of the cryptocurrency start-up Lightning Labs, was not affiliated with the lab but knew Mr. Ito and several others there. When she was raising money for her company in 2015, someone at the lab contacted her and offered to invest Mr. Epstein’s money. Ms. Stark found a news article about Mr. Epstein’s history and turned it down.

“In five minutes I was able to Google and make a determination that seemed like such a no-brainer,” she said.