A man's voice cut through the rain that lashed the black Caribbean Sea, barely audible between two ships tossed about by three-meter waves.

The people on the smaller boat, a simple fishing skiff, held their cell phones like emergency flares in the night. The larger vessel approached.

A figure wrapped in a bulky jacket and a black cap waved her arms. It's me, Maria.

Venezuelan opposition leader María Corina Machado had just endured the most dangerous stage of her escape from her homeland on her way to receive the Nobel Peace Prize in Norway. It was early Tuesday morning when the extraction team rescued her. Part of the rescue was captured on video seen by The Wall Street Journal.

For the past three hours, Machado and a small crew had been adrift in a small boat in the Gulf of Venezuela after her GPS fell overboard in rough seas and a backup failed. She didn't meet the rescue team at a designated pickup point, prompting a race to find her in treacherous waters.

Bryan Stern, a bearded American combat veteran sent to extract Machado from Venezuela, said he brought her aboard the larger boat and gave her snacks, Gatorade, and a dry sweater. He alerted his team that Machado was on board: Jackpot, jackpot.

In a proof-of-life video sent to U.S. officials and shared with The Wall Street Journal, Machado tries to calm herself as the boat rocks on the waves. “My name is María Corina Machado,” she says, “I am alive, safe, and very grateful.”

Stern, who heads an organization specializing in these types of extractions, composed of former special operations and intelligence veterans, named the mission Operation Golden Dynamite. This is a reference to the Nobel Peace Prize and its founder, Alfred Nobel, the Swedish chemist who invented dynamite.

New details from Stern and another person familiar with the operation, as well as timestamped text messages, videos and photos of the mission reviewed by The Wall Street Journal, paint a picture of a dangerous expedition that nearly failed.

Stern said he was in constant contact with senior U.S. military officials before and during the operation: sharing his live location, describing roadblocks, sending updates, and at one point asking if the military could detect Machado's boat when they had lost communication with him.

The State Department and the Pentagon referred the questions to the White House. The White House did not respond to requests for comment.

The operation was funded by private donors, Stern said, without any U.S. government funding. But U.S. officials—from the White House to senior military officers and regional diplomats—tracked the journey in real time through WhatsApp messages and voice memos from Stern and his team.