But nearly 18 years later, he continues to treat the ravaged mouths of professional hockey players as the team dentist of the Tampa Bay Lightning.
"I basically walked into it, and I think for me, that was a bit of a shock," Dr. Rivera said. "It was a lot of pressure because I was right out of school pretty much, and here I am, taking care of a hockey team, a national hockey team."
Dr. Rivera, 44, first started helping with the team in 2002, a few months after he joined the Tampa, Florida, dental practice of Drs. Sam and Vince Caranante, two brothers who were the Lightning's team dentists. When Dr. Rivera purchased the practice from the brothers in January 2007, he became the team's main dentist.
"I definitely had to learn the sport," he said. "It was not something I thought I'd ever end up doing, but I love doing it. Now, I love the game. Now, I'm like an insane, fanatical hockey fan."
Most of the work he does for the Lightning revolves around treating what commonly results from blunt-force trauma to the mouth, like chipped, knocked-out and necrotic teeth and temporomandibular joint dysfunction. But he has seen some extreme cases as well.
In December 2007, Tampa Bay Lightning winger Craig MacDonald took a puck to the mouth, knocking out his teeth, exposing nerves and leaving his tongue hanging on by a thread. The damage required multiple sutures, root canals and multi-unit bridges to fix.
"When I looked at his mouth, it was all traumatized," Dr. Rivera said. "The blood coagulate had covered all his teeth, and it actually looked foreign to me because I couldn't see any normal anatomy, like gingiva, teeth. It was just a mess in there."
It's hard to know exactly what he'll face in any given day, so Dr. Rivera tries to be ready for anything. That means having whatever he might need with him in his portable kit to provide quick, stabilizing care on the scene, from local anesthesia to temporary cement. More extensive work has to wait until later.
"Those guys don't want to spend time having the dentist look at them; they just want to get back on the ice," Dr. Rivera said.
One of the biggest challenges of Dr. Rivera's dual career with the NHL and his private practice is the long days. He often finds himself working a full day at his office and then switching gears to cover a hockey game for another five-plus hours.
But despite those long days, Dr. Rivera appreciates being part of the team, which comes with certain perks, like getting to celebrate the Lightning's Stanley Cup win in 2004.
"It's a lot of fun to be part of a team," he said. "Especially if you're going to be a dentist, an NHL team is probably the pinnacle of any sport that you'd want to be involved in."