“I’ve never met Jared Kushner,” said Dore Gold, a longtime adviser to Mr. Netanyahu who recently stepped down as director general of the Foreign Ministry. Neither had Sallai Meridor, a former ambassador to the United States; Yaakov Amidror, a former national security adviser to Mr. Netanyahu; or Avinoam Bar-Yosef, president of the Jewish People Policy Institute, a Jerusalem-based group that researches Israeli-American relations. Nor had the main opposition leaders Isaac Herzog and Yair Lapid.

Still, Mr. Kushner has been Mr. Trump’s intermediary with a variety of important Israeli and Jewish American players, including Mr. Netanyahu, Mr. Dermer and wealthy donors like Sheldon Adelson, the Nevada casino magnate. He brokered a meeting between Mr. Trump and Mr. Netanyahu in September and sat in on it.

“He follows the issue. He’s a strategic thinker,” said Martin Peretz, the former owner and editor in chief of The New Republic, who met Mr. Kushner at Harvard University and now splits his time between Israel and the United States.

“Does he know enough? Does he know more than Aaron David Miller? Probably not. Does he know more than Dennis Ross? Probably not,” Mr. Peretz said, naming two longtime American negotiators. But “he certainly knows more about the area than Barack Obama, and more than John Kerry.”

The grandson of Holocaust survivors, Mr. Kushner was raised in an Orthodox Jewish household in New Jersey and graduated from a Jewish day school before attending Harvard. He observes the Sabbath, and his wife — Mr. Trump’s daughter Ivanka — converted to Judaism before their marriage. Mr. Trump’s transition team would not say how often Mr. Kushner visited Israel or whether he had any Palestinian connections. But an aide to the president-elect emphasized that Mr. Kushner would be just one of many advisers on the Middle East.

Mr. Kushner, who took over his family’s real estate empire in his 20s and bought The New York Observer, visited Israel in 2014 when he was trying to acquire a controlling stake in Phoenix Holdings, an insurer. He signed a nonbinding memorandum of understanding to buy 47 percent of the firm from the Delek Group, an Israeli conglomerate, for about $434 million. But the deal fell apart, partly because of regulatory requirements.

Mr. Kushner was in Israel during the war with Gaza that summer, which seemed to unnerve his wife. “We have small children, and Ivanka didn’t like the idea of me being here,” he told the Israeli newspaper Yedioth Ahronoth. “As an American who listens to the news every hour, and hearing about 90 missiles hitting Israel on a daily basis, she asked me, ‘What the hell are you doing?’”