Thousands of people who had spent days stranded at the Burning Man festival in a rain-gorged stew of mud and slop began to pack up their camps on Monday and stream away from the sprawling site in remote northwest Nevada.

“Exodus operations have officially begun,” organizers wrote in a post on social media.

But it was a mucky, uncertain trek. The ancient lake bed where the annual festival is held was beginning to dry and harden on Monday after days of torrential rain, but drivers said they were still encountering foot-deep puddles and stretches of muddy bog along the five-mile route from the camp to a paved road.

“You had to haul,” said Kristine Rae, 50, a physical therapist from Idaho who made it out in her truck. On her way, she saw marooned vehicles that weren’t so lucky. “There were cars stuck halfway up their wheels.”

Even in normal years, leaving Burning Man can take up to 12 hours as thousands of cars and trailers creep off the desert playa and onto a jammed two-lane road. This year, organizers urged the roughly 72,000 attendees to consider postponing their departure until Tuesday to avoid creating an epic traffic jam.

On Monday, Black Rock City — the name of the site on federal lands where the annual celebration of arts and music takes place — was a hive of activity as people packed sleeping bags, stoves and muddy tents into their trunks before heading out. Some left excess water, food and camping essentials for festivalgoers — known as burners — who were staying.

Roughly a third of the campers had packed up and moved out, and others were collecting mud-caked flotsam left behind in the rutted ground. There were abandoned bikes, mud-smothered tents and the steel skeleton of a 15-foot shade structure. At camps, people raked the ground to search for any items that had become mixed into the hardening batter of dirt and rain.

Some people had decided to stay in the hope that an improved weather forecast on Monday night would allow for Burning Man to stage the festival’s twice-postponed climax: the burning of a towering wooden effigy shaped like a man.

“Of course I’m staying,” said Olivia Steele, 38, an artist whose trailer had become home to a half-dozen other campers fleeing their leaking tents. “We come here every year to get schooled. This time we got a great education.”

Muddy conditions and the inability to move heavy fire safety equipment to the burning site were to blame for the delays, officials said on a social media account linked to the festival.

It was a welcome change from the downpours that began on Friday and forced the festival to urge attendees to shelter in place and conserve food and water.

Bike wheels became clogged with mud, and people had to navigate the normally powdery desert with plastic bags over their shoes to protect them from the oatmeal-thick mud. Some decided to bail, trudging through miles of mud to reach the road and hitchhike. A widely shared video showed the music producer Diplo and the comedian Chris Rock sandwiched in the back of a pickup truck after being picked up by fans.

The makeshift town of Black Rock City hosts more than 70,000 people every year and is a three-hour drive from the nearest airport, which is more than 100 miles away in Reno. This year’s festival began on Aug. 27.

The authorities were also investigating the death of one participant, though they said it did not appear to be weather-related.

In normal years, people at the festival have to contend with sweltering temperatures and dust storms, so this time, many tried to embrace the mud. Donovan McGrath, a 47-year-old yoga instructor from Los Angeles, said that many at the camp threw parties inside recreational vehicles, played games and got to know the people they were stuck indoors with.

“The rain provided an amazing opportunity to walk, to move more slowly, to connect with people who you may not have,” he said. “There were many silver linings.”

On Sunday afternoon, a White House official said President Biden had been briefed on the situation and that administration officials had been in touch with state and local officials. On the playa, people laughed about the fact that the president had been briefed about Burning Man, Mr. McGrath said.

Mayor Hillary Schieve of Reno said Sunday on social media that the city was working with regional partners to prepare for a mass exodus of Burning Man attendees. Certain parking lots of the local convention center were available for use, she said.

Many said the unexpected rain had brought out the gritty, self-reliant roots of a festival that has sometimes been criticized for gentrifying into a destination party for tech moguls and social-media influencers. On Monday afternoon, tents were coming down and a bus was expected to arrive at the 100-person Mystopia camp where Hayden Welda had stayed during the festival. He and his crew were already talking about their return.

“We’ll be back next year,” he said, “and hoping it doesn’t rain.”

Ernesto Londoño, Anna Betts and Amanda Holpuch contributed reporting.