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. On Monday morning, salvage crews began the arduous task of trying to refloat the ship so they can move it to the Italian port of Genoa to be dismantled.
By midday Monday, the ship was floating again, Costa Crociere CEO Michael Thamm said.
It's been more than two and a half 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 the past 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 shift to the east. After 30 meters, divers will begin attaching more chains and cables to help reinforce the bottom.
Then the full refloat begins, lifting the Concordia, deck by deck, clearing any debris along the way.
CNN's Barbie Latza Nadeau said the 20-meter shift had taken place earlier than planned and had already dramatically changed the appearance of the wreck from land.
"There is no break, it's a 24-hour process, but the fact that they are ahead of schedule means this could go fast," she said.
Once the ship is completely floated, it will be towed -- slowly and carefully -- 240 kilometers (150 miles) to Genoa.
Officials say 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 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 -- and that doesn't include the refloat, the anticipated transport to Genova 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 last October. But the body divers found turned out to be Maria Grazia Trecarichi, a Sicilian who had been on the cruise to celebrate her 50th birthday with her 17-year-old daughter, who survived.
Journalist Barbie Latza Nadeau reported from Giglio. CNN's Erin McLaughlin reported from London, and CNN's Catherine E. Shoichet reported from Atlanta.
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