Florencio Avalos, 31, emerged from the Phoenix II capsule to an ovation from those gathered at the scene of the rescue -- including his wife and a young son -- which was televised around the world.
Avalos got into the capsule after a rescuer, Manuel Gonzalez, was lowered into the mine. Plans called for three more rescuers to be lowered during the rescue of the remaining miners, which was expected to take as much as 48 hours.
Gonzalez, is an expert in mine emergencies and vertical ascents, the Santiago Times reported. Television news organizations aired live pictures of Gonzalez emerging from the capsule to a warm greeting from the trapped miners.
The move followed a test run of the capsule designed to pull the miners to safety one at a time, The New York Times reported.
Government officials said rescue workers had made quicker progress than expected, and the men could begin coming out up to 6 hours earlier than previously estimated, as early as 6 p.m. local time (5 p.m. Eastern time), the Times said.
Marta Mesias, 51, the aunt of miner Claudio Yanez, 34, said she had traveled from Santiago to witness the rescue of her nephew.
"We're going to toast him with champagne, and feed him a bit of roasted chicken," she told the Times.
Chilean President Sabastian Pinera, who was expected to be on hand, had said he was looking forward to seeing the men reach the surface of the mine near Copiapo.
"I hope that by tomorrow (Tuesday) or Wednesday, the miners will not only be able to see sunlight, but embrace their wives and girlfriends, parents, mothers and children," Pinera told CNN en Espanol Monday. "We have been with the miners since the accident and will remain with them once they are rescued."
Chilean Mining Minister Laurence Golborne had said earlier rescue workers hope to begin the extraction Tuesday night or early Wednesday.
"We're going to take all the time necessary to assure that the plans are adequate," no matter when the process begins, Golborne said.
Alejandro Pino, regional manager of the Chilean Safety Association, showed reporters the gear the miners will use once they begin to be individually lifted to the surface in a rescue capsule dubbed the Phoenix. Each miner will receive moisture-resistant green coveralls embroidered with their names, and fresh pairs of socks and underwear.
Rescue planners said they want the first men brought to the surface to be healthy and prepared to handle any problems that could arise as the capsule makes its trip up, The Washington Post reported. Officials said the first man out could be Florencio Avalos, 33, who is healthy, experienced and relatively young.
Doctors said they will monitor the miners' heart rate and blood pressure as they are brought to the surface.
"The biggest risk is probably fainting" and possibly panic attacks, said Jean Romagnoli, a doctor who has been monitoring the miners' health.