(CNN) -- A world mesmerized by a 68-day tale of true grit expects a joyful ending Tuesday in a desolate patch of Chile's Atacama Desert.

One by one, 33 miners, trapped in a gold and copper mine since the start of August, will put on green coveralls made of moisture-resisting material and personalized with names like Raul Enriquez Bustos Ibanez. Juan Illanes Palma. Alex Vega Salazar.

The oldest is 63. The youngest, only 19.

Rescuers at the Chilean mine said the concrete base built for the winch system at the San Jose Mine had hardened, paving the way for the rescue of the miners to begin late Tuesday.

"We hope to finish the day with at least one miner on the surface," said Mining Minister Laurence Golborne.

The miners will also have on fresh underwear and socks when they climb into a claustrophobic capsule only a little wider than the span of their shoulders.

They will be instructed on the communications equipment and the oxygen supply inside the rescue tube. And they will put on special goggles to protect their eyes -- which have become accustomed to the vampiric darkness of the caved-in mine -- from the lights up above.

Then the order to hoist will ring out and each man will begin a slow, bumpy, upward journey through half a mile of rock.

Each time a miner comes out, a siren, like that of an ambulance, will sound. Chilean Health Minister Jaime Manalich told families not to panic when they heard the siren. In this case, it was not being used for something bad, he said. Only to herald the arrival of a moment as joyous as a baby's entrance into he world.

The miners have been placed on liquid diets in case they vomit on the way to the surface and they have been exercising for an hour a day.

Yonni Barrios, is a paramedic and has been weighing his fellow miners daily, taking blood tests and doing daily urine analyses. The others call him "Dr. House" after the television show, which is popular in Chile.

It's unclear exactly when the rescue will begin, but it is likely to go from night into day. Some of the men will feel the intense chill of a desert night; others may come out to a searing sun burning high in a cloudless sky.

The rescue capsule will spin as it rises. It will be harrowing. And dark. Like a scary amusement park ride.

Except the thrill for these 33 men will lie at the end of the ride, when each will see the families they probably feared they would never see again.

"As he comes out he will be reborn," said Nelly Bugueno about her son Victor Zamora Bugueno, 33, who helped handle the cylinders -- called carrier pigeons -- that brought food and other supplies to the trapped miners. Her son is also a poet.

Nelly Bugueno has been camping out with the other families above the caved-in mine in this spartan area void of hotels, gas stations or any other amenities. They named the place Camp Esperanza (Hope).

Tuesday, that hope was apparent as the families sang songs and could not contain the joy of long-awaited reunions.

Children played soccer in front of a red school house erected at the camp and 33 flags -- 32 Chilean and a single Bolivian -- representing the nationalities of the men buried underneath.

"God is in all places, At the same time your family loves you," read a sign for Mario Nicolus Gomez Heredia, the oldest of the miners.

Gomez began mining at the tender age of 12. He became a spiritual leader for the trapped men and requested a crucifix and statuettes of saints so the men could construct a shrine inside the mine.

But amid hope also lurked fear. What if something went wrong? Claudio Lobos craved reassurance.

His brother Franklin Lobos Ramirez, 53, once played soccer in a Chilean professional league and served as an an electrician in the mine. The mine collapsed as he and Jorge Hernan Galleguillos Orellana drove a truck deep down inside the shafts. They slowed down to look at a small white butterfly that had somehow gotten in the mine, and just ahead of them the rocks began caving in. It saved their lives, they said.

If only the journey back was guaranteed to be as lucky. The rescue cage looked small to Claudio. Would his brother fit in there? Was it safe? he asked journalists.

He was told the Chilean government has used every resource to save his brother. What more could journalists say?

The first to come out will be five miners who have been deemed fit and who possess the most technical know-how so that they can advise the rescue teams.

The next five will be the physically weakest, a term perhaps not appropriate for anyone who has survived more than two months in the bowels of the earth. But one of the miners has diabetes; another has black lung.

The last to come out will be Luis Alberto Urzua Iribarren, 54. Like the captain of a sinking ship, the shift supervisor volunteered to stay behind until all his men were safe.

Once the men have been extracted, they will undergo about two hours of health checks at a field hospital set up at the mine. They will then be flown by helicopter to a hospital in the town of Copiapo -- approximately a 15-minute flight.

Miners who are healthy enough will be allowed to visit briefly with family members in a reunion area before being taken to the hospital. Some have exhibited anxiety, according to Manalich, the health minister. They may experience psychological problems.

For the 33 men, the only contact with the outside world since the beginning of August was through a small bore hole through which they were sent food, water and other supplies. A letter sent by one of them said they would take a vow of silence, to never to fully reveal the details of their underground misery.

Edison Fernando Pena Villaroel, 34, sent back a request for Elvis Presley music and led the group in sing-alongs.

Victor Antonio Segovia Rojas, 48, kept a journal throughout the ordeal and sent his updates to help keep the rescuers on the surface informed about the miners' well-being. He's an acoustics expert.

Jimmy Sanchez Lagues, 19, the youngest miner who worked as an environmental assistant sent a letter to his mother. He just wanted to taste her cooking again.

Ariel Ticona Yanez, 29, watched his wife give birth to a baby girl via a video link that was lowered into the mine. Of his three children, this was the first birth he was able to witness. They called their new daughter Esperanza.

High above the miners, the buzz of electrical generators brought in by hordes of media began to drown out other sounds Tuesday. About 1,500 journalists from 39 nations gathered to tell a story of survival.

On this sweltering desert day, the entire world was watching with hope in their hearts for a very happy ending.

CNN's Karl Penhaul, Patrick Oppmann, Gary Tuchman and Luis Carlos Velez contributed to this story.