Kayla Thompson and her husband, Kasey Thompson, were asleep in their R.V. camper at their first Burning Man festival on Wednesday morning when she awoke in pain. She thought it might be something she ate, or worse, her appendix.

The rain had stopped, but the desert playa that stretched infinitely around their camper was mucky and filled with puddles from a storm that had pummeled the Southwest. Ms. Thompson’s cramping was unrelenting. The couple knew they needed medical help, but they did not anticipate what would happen next: Minutes later, Ms. Thompson was giving birth to their first child, a 3-pound, 9-ounce baby girl, in the bathroom of their camper.

The couple had not been planning for a child and had no idea that Ms. Thompson was pregnant.

“Even the nurses at the hospital were like, ‘You don’t look like you were pregnant at all,’” Ms. Thompson, 37, who works in medical billing, said, adding, “I didn’t have any symptoms.”

After Ms. Thompson delivered the baby, Mr. Thompson ran out of the R.V. and desperately called for help, he said. “I was yelling for anyone to come help us,” Mr. Thompson, 39, who lays tiles, recalled through tears.

Within minutes, a neonatal care nurse, a pediatric doctor and an obstetrician-gynecologist, among other festival attendees from nearby camps, filled their camper. The man who identified himself as an OB-GYN was wearing nothing but his underwear as he helped Ms. Thompson deliver the placenta.

“This should not be happening this way,” Mr. Thompson recalled thinking. He raced around in search of supplies and relied on the community of Burners, many of them strangers from nearby camps, as he and his wife experienced some of the scariest moments of their lives. Had it been an hour earlier or an hour later, Mr. Thompson estimated, the couple would have been stranded at the camp because of the weather.