“You have this town where death is common and there are terrifying things that are coming at every second, and everybody is ok with it and gets on with their lives,” he said. “In Night Vale it’s aliens, and in real life it’s cancer.”

He found eager collaborators in Mr. Cranor and Mr. Baldwin, who plays the deadpan narrator, Cecil Gershwin Palmer. Both were writers and performers in an experimental theater group, the New York Neo-Futurists, with Meg Bashwiner, who is married to Mr. Fink. He and Mr. Cranor had written a play together about time travel, and shared a wry, offbeat sense of humor.

When the first episodes were posted in June 2012, they barely generated a ripple.

“At the time, I don’t think I could even get my mom to listen to the podcast,” Mr. Baldwin said. “She was like, ‘Oh, another nonpaying job, that’s great, sweetie.’ ”

They kept at it, posting a new 25-minute episode every other week. Over the next year, the show was downloaded roughly 150,000 times.

Then, for reasons its creators still can’t fully explain, the audience exploded overnight. In July 2013, the show was downloaded 2.5 million times. It shot to the No. 1 spot on iTunes, surging ahead of popular programs like “This American Life” and “Radiolab.” That August, it was downloaded 8.5 million times. Rabid fans were obsessively dissecting each episode on sites like Reddit and Tumblr.

“The Internet wouldn’t stop talking about it,” said Ransom Riggs, author of the best-selling novel “Miss Peregrine’s Home for Peculiar Children,” who became a fan of the podcast after seeing repeated references on Twitter. “It’s got a ‘War of the Worlds’ thing going on where if you didn’t know anything about it, you might think you stumbled on an actual small town radio station.”

Mr. Fink and Mr. Cranor were besieged with offers from TV producers, filmmakers and publishers seeking spinoff projects. Audiences flocked to their live shows.