Giglio, Italy (CNN) -- The last time anyone saw Russel Rebello alive, he was near the stern of the Costa Concordia, helping passengers into rescue boats.
But the 33-year-old waiter from India never escaped the doomed cruise ship. And he's the only victim of the 2012 shipwreck whose remains haven't been found.
Investigators hope that could change soon. A complicated operation to refloat the ship gives them a chance to begin a new search for Rebello.
By midday Monday, the ship was floating again, Costa Crociere CEO Michael Thamm said.
Salvage crews began the arduous task of refloating the ship on Monday morning so they can move it to the Italian port of Genoa to be dismantled.
It's been more than 2½ years since the ship ran aground off Italy's Giglio Island with more than 4,200 passengers aboard, killing 32 people in a disaster that drew global attention.
And it's been 10 months since salvage teams rolled the 114,000-ton vessel off the rocks in one of the most complex shipwreck recovery efforts ever undertaken.
But there's still more work to be done.
"We are not at the end, but we are at a critical moment," Giglio Mayor Sergio Ortelli told reporters.
For 10 months, engineers have been hard at work, attaching metal boxes to either side of the ship.
After draining water from the boxes, they had to pump compressed air into its place to get the ship to float.
It was a dangerous and tricky procedure. The ship is rotting, and there's a real risk the bottom of it could give way.
By lunchtime Monday, the ship had been moved 20 meters (about 66 feet) as part of an initial 30-meter (98-feet) shift to the east.
The shift dramatically changed the appearance of the wreck from land.
After 30 meters, the ship will be anchored and operations will cease for Monday.
On Tuesday, five steel hollow boxes, or sponsons, will be lowered, and divers will begin attaching more chains and cables to help reinforce the bottom of the boat.
Once that's done they'll raise the ship deck by deck, clearing any debris along the way.
After the ship is completely floated, a convoy of 10 boats will then begin a potentially treacherous journey.
The ship will be towed -- slowly and carefully -- 240 kilometers (150 miles) to Genoa.
Italian Environment Minister Gian Luca Galletti told the media that the operation marked the closure of a dark moment in Italy. He said it would have been too dangerous to leave the Costa Concordia in the same position for another year.
"We could have dismantled the Concordia in situ, but they chose to take the more expensive, riskier route to tow it away to save the environment of Giglio," Galletti said.
Officials said it's likely the towing process won't start for days due to port restrictions. It will take five to six days for the ship to reach Genoa, officials said.
Thamm, the CEO, called the operation "the most daunting salvage ever attempted on a ship of its size."
He added that the cost of the project has already exceeded 1 billion euros -- not including the refloat, the anticipated transport to Genoa or the dismantling.
Since the wreck two years ago, 24 metric tons of debris -- including furniture, dishes, food, personal effects and ship parts -- have been recovered from the seabed.
While salvage crews continue efforts to deal with the wreckage, Francesco Schettino, the ship's captain, is on trial on charges of manslaughter, causing a maritime disaster and abandoning ship with passengers still on board. He denies wrongdoing.
Search teams thought they had found Rebello's remains in October. But the body divers found turned out to be that of Maria Grazia Trecarichi, a Sicilian who was on the cruise to celebrate her 50th birthday with her 17-year-old daughter, who survived.
In a Facebook post, brother Kevin Rebello said he was watching the latest salvage operation live online, since he couldn't make it to Giglio.
"I strongly believe that they will find the body of my dear brother," he said.
Journalist Barbie Latza Nadeau reported from Giglio. CNN's Erin McLaughlin reported from London, and CNN's Catherine E. Shoichet reported from Atlanta.