- The ship is now floating again, the Costa CEO says
- The Costa Concordia cruise ship ran aground and tipped in January 2012, killing 32 people
- Officials hope to find the remains of waiter Russel Rebello, only victim not found
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.
Costa Concordia floats again 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.
Two and a half years after it ran aground off Giglio, Italy, crews began to raise the Costa Concordia cruise ship from the seabed on Monday, July 14. 
Crews raised the stricken ship several meters in the first six hours of the re-floating operation on July 14. 
Thirty-two passengers and crew died when the 114,000-ton vessel struck the rocky outlay surrounding Giglio in January 2012. 
Crews will check the decaying cruise liner for leaks over the next few days, before towing it north to the port in Genoa, Italy. 
In December 2013 crews managed to "parbuckle" (rotate upright) the Concordia, seen here on Friday, July 11, but weather conditions meant the ship could not be floated and towed away until now. 
Crews attached 30 steel tanks to the Concordia and are filling them with compressed air to float the ship, seen here on June 26. 
Francesco Schettino (L), the ship's captain, returned to the Concordia in February 2014 for the first time since he ran the liner aground. He faces multiple charges over the incident, including manslaughter and abandoning ship. 
Experts inspect the wreck of the ship on January 23. The delegation boarded the vessel to collect new evidence, focusing on the ship's bridge and the on-board elevators. 
The wreckage of the Costa Concordia cruise ship sits near the harbor of Giglio, Italy, on Tuesday, September 17, after a salvage crew rolled the ship off its side. 
The ship had been lying on its side for 20 months off the island of Giglio. Here, members of the U.S. company Titan Salvage and the Italian marine contractor Micoperi pass by the wreckage. 
Damage to the right side of the ship is apparent in the early hours of September 17. 
Using a vast system of steel cables and pulleys, maritime engineers work on Monday, September 16, to hoist the ship's massive hull off the reef where it capsized. 
The project to upright the Costa Concordia continues on September 16. The nearly $800 million effort reportedly is the largest maritime salvage operation ever. 
A water line marks the former level of the stricken Costa Concordia as the salvaging operation continues on September 16. The procedure, known as parbuckling, has never been carried out on a vessel as large as Costa Concordia before. 
Members of the U.S. salvage company Titan and Italian firm Micoperi work at the wreck site early on September 16. 
Technicians work to salvage the half-submerged ship on July 7. Nearly 500 workers are involved in an operation to remove the wreck while protecting the marine environment. 
Giant hollow boxes have been attached to the side of the ship, seen on May 27, 2013. Attempts to refloat the ship will be aided by the compartments. 
A commemorative plaque honoring the victims of the cruise disaster is unveiled in Giglio on January 14, 2013. 
Survivors, grieving relatives and locals release lanterns into the sky in Giglio after a minute of silence on January 13, 2013, marking the one-year anniversary of the shipwreck. The 32 lanterns -- one for each of the victims -- were released at 9:45 p.m. local time, the moment of impact. 
A man holds an Italian flag on his balcony overlooking the port of Giglio on January 13, 2013. 
A man works in front of the shipwreck on January 12, 2013. 
A couple walks along the port of Giglio at night on January 12, 2013. 
A man sits in his boat in front of the half-submerged cruise ship on January 8, 2013. 
Cranes and floating decks surrounding the ship light up the dusk sky on January 9, 2013. 
Workers stand on the edge of the ship on January 8, 2013. 
A crew passes by the hulking remains on January 7, 2013. 
People enjoy a day in the sun with a view of the cruise liner on July 1, 2012. 
Military rescue workers approach the cruise liner on January 22, 2012. 
Members of the Italian coast guard conduct a search-and-rescue mission on January 21, 2012. 
Rescue operations to search for missing people resumed on January 20, 2012, after being suspended for a third time as conditions caused the vessel to shift on the rocks. 
The Costa Serena, the sister ship of the wrecked Costa Concordia, passes by on January 18, 2012. 
A bird flies overhead the Costa Concordia on January 18, 2012. Rescue operations were suspended as the ship slowly sank farther into the sea. 
The ship was sailing a few hundred meters off the rocky Tuscan coastline. 
An Italian coast guard helicopter flies over Giglio's harbor on January 16, 2012. 
Rescuers search the waters near the stricken ship on January 16, 2012. 
The Concordia, pictured on January 15, 2012, was on a Mediterranean cruise from Rome when it hit rocks off the coast of Giglio. 
The ship starts keeling over early on January 14, 2012. Evacuation efforts started promptly but were made "extremely difficult" by the position of the listing ship, officials said. 
Rescued passengers arrive at Porto Santo Stefano, Italy, on January 14, 2012. The Costa Concordia was carrying 3,200 passengers and 1,000 crew members. The Costa Concordia disaster
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See inside underwater cruise ship 
Costa Concordia's painful legacy 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.
We are not at the end, but we are at a critical moment.
Giglio Mayor Sergio Ortelli
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.
Nine things to know about the plan to salvage the Costa Concordia
Journalist Barbie Latza Nadeau reported from Giglio. CNN's Erin McLaughlin reported from London, and CNN's Catherine E. Shoichet reported from Atlanta.
