Videos on social media showed Laura’s winds battering a tall building in Lake Charles, blowing out windows as glass and debris flew to the ground.
Hours after landfall, the wind and rain were still blowing too hard to check for survivors.
NBC News' Jay Gray reports from Louisiana
Dick Gremillion, the emergency director in Calcasieu Parish, said hours after landfall that they hadn’t been able to get out and look for damage.
“The wind is still over 50mph.
"It’s going to have to drop significantly before they can even run any emergency calls. We also need daylight,” Mr Gremillion said.
Tony Guillory, president of the Calcasieu Parish Police Jury, described the scene early on Thursday morning over the phone as he hunkered down in a Lake Charles government building that was shaking from the storm.
“There are some people still in town and people are calling… but there is no way to get to them,” he said.
He said he hopes those stranded can be rescued later on Thursday, but he fears blocked roads, downed power lines and flooding could delay that process.
Authorities had ordered coastal residents to evacuate ahead of the incoming storm, but not everyone did in an area that was devastated by Hurricane Rita in 2005.
“We know anyone that stayed that close to the coast, we’ve got to pray for them, because looking at the storm surge, there would be little chance of survival,” Louisiana Lieutenant Governor Billy Nungesser told ABC’s Good Morning America.
With more than 290,000 homes and businesses without power in Louisiana and neighbouring Texas, near-constant lightning provided the only light for some.
Officials said search and rescue missions would begin as soon as conditions allow, along with damage assessments.
The National Hurricane Center said Laura slammed the coast with winds of 150mph (241 kph) at 1am (7am BST) as a Category 4 hurricane near Cameron, a 400-person community about 30 miles east of the Texas border.
Hours after landfall, Laura was still a Category 2 hurricane, with maximum sustained winds of 110 mph (175 kph) and forecasters warned it still has "extremely dangerous" winds.
“Unsurvivable storm surge with large and destructive waves will cause catastrophic damage,” forecasters warned.
“This surge could penetrate up to 40 miles inland from the immediate coastline, and flood waters will not fully recede for several days,” the hurricane center said.
Its centre was past Lake Charles, moving north at about 15mph (24kph), but with damaging winds that stretched over much of Louisiana and parts of eastern Texas, reaching as far as 175 miles (280 kilometres) from Laura’s centre.
Forecasters said the storm surge could reach 15-20 feet in Port Arthur, Texas, and a stretch of Louisiana including Lake Charles.
They expect Laura to move north through Louisiana and cause widespread flash flooding in states far from the coast.
After turning east and reaching the Atlantic Ocean, it could again become a tropical storm and threaten the north-east states.
More than 580,000 coastal residents were ordered to join the largest evacuation since the coronavirus pandemic began and many did, filling hotels and sleeping in cars since officials didn’t want to open mass shelters and worsen the spread of Covid-19.
But in Cameron Parish, where Laura came ashore, Nungesser said 50 to 150 people refused pleas to leave and planned to weather the storm in everything from elevated homes to recreational vehicles.
The result could be deadly, since some houses weren’t raised high enough to withstand the massive storm surge.
“It’s a very sad situation,” said Ashley Buller, assistant director of emergency preparedness.
“We did everything we could to encourage them to leave.”
Laura hit the US after killing nearly two dozen people on the island of Hispaniola – 20 in Haiti and three in the Dominican Republic.
Laura is the seventh named storm to strike America this year, setting a new record for US landfalls by the end of August. The old record was six in 1886 and 1916, according to Colorado State University hurricane researcher Phil Klotzbach.