AMANDA NUNES arrives by skateboard for her first training session of the day, smiling and sweating lightly in denim cutoffs and a ripped T-shirt. The UFC women’s bantamweight champion seems genuinely thrilled to see every person she encounters inside American Top Team, a mixed martial arts gym in Coconut Creek, Fla., about 20 miles north of Fort Lauderdale. The 40,000-square-foot space looks like a warehouse and feels like a sauna thanks to dozens of overheated fighters who hit bags and pads, grapple on the mats and spar inside the octagon.

“I...