Red Bull's Verstappen started the season in dominant fashion, winning four of the first five races to be seemingly set to wrap up his fourth drivers' title well before the end of the campaign.
The Dutch 27-year-old, who won 19 of 22 races last year, has failed to win any of the last eight, however, with McLaren's Lando Norris his closest challenger and now 52 points behind with six rounds remaining.
"Our ticket sales really took off when Max stopped winning, and it got more competitive," Epstein, whose Circuit of the Americas (COTA) hosts a sprint race weekend on October 19-20, told reporters.
The promoter had feared a "weakest year in four since the pandemic" but said there had instead been a 'hockey stick' effect of sales trending upwards.
The Grand Prix will also be the first since Red Bull-owned RB dropped Australian Daniel Ricciardo, a big favourite of the US crowd, last month and replaced him with New Zealander Liam Lawson.
Epstein hoped Ricciardo might still attend in some other role. "I'm not sure necessarily people are buying tickets to come see him race if he's not in a competitive car, right?" he said.
"If you're coming, though, because he's part of the F1 community, I think he can still be part of the F1 community in a pretty meaningful way. And he's really, really loved in Texas, and I think he likes it here.
"I hope he's still coming here because we've got a lot of people that would love to shake his hand or get his autograph or take a picture or just see him around town. We'll keep him busy."
The circuit will be hosting an Eminem concert after the Saturday sprint and Epstein expected a crowd of 130-150,000 on that day alone.
There will also be a college football game in town on the Saturday between the Texas Longhorns and the Georgia Bulldogs, a heavyweight clash that has sent hotel prices soaring in the state capital.
"I think we'll have a weekend like we've never had before in terms of overall excitement and things to do," said Epstein.
"The fact that we've got the top-ranked college game happening on that Saturday is going to make for an amazing weekend."