Recent Treasury secretaries with Goldman roots include Robert E. Rubin, a former co-chairman, under Bill Clinton; and Henry M. Paulson Jr., a former chairman and chief executive, under George W. Bush.

Even in the Obama administration, where a Goldman pedigree was something akin to a scarlet letter, Gary Gensler was credited with reviving a moribund Commodity Futures Trading Commission and might have been Treasury secretary had Mrs. Clinton won in November.

Which raises the question: Why would such a disproportionate number of the “best people,” in Mr. Trump’s view, come from just one bank? After all, Goldman is hardly the only large bank, and it is also far from the biggest. It employs roughly 33,000 people; JPMorgan Chase’s work force is many times as large.

Many point to a unique Goldman culture that has long encouraged public service and philanthropy as integral to its business model.

Goldman “does seem to produce people who are very smart and have valuable experience,” Mr. Bloomberg said. “And they have a culture and a long tradition of leaving the firm for public service. The firm pushes them to do that.”

Mr. Cohn would seem to be a good example. After 26 years at the firm, most recently as president and chief operating officer, he sought out Mr. Trump once it became clear that Goldman’s chief executive, Lloyd C. Blankfein, had no immediate plans to step down.

Mr. Cohn would hardly seem an obvious choice for the Trump administration — he is a registered Democrat and had no past relationship with Mr. Trump. But he knew Jared Kushner, Mr. Trump’s son-in-law, and after several face-to-face meetings, Mr. Trump was won over by Mr. Cohn’s innovative ideas for financing infrastructure projects and his up-by-the-bootstraps biography: Mr. Cohn, the son of an Ohio electrician, overcame dyslexia and taught himself options trading before talking his way into a position at the New York Mercantile Exchange. (Mr. Cohn declined to comment.)