He was a three-time NCAA champion at Ohio State and has won three world championships.
Now 28, Snyder looks to add to his legacy at the Paris Olympics. If he wins gold in the 97-kilogram freestyle category, he would join George Mehnert, John Smith and Bruce Baumgartner as the only American two-time gold medalists.
He says he's his best version of himself heading into Paris.
"My body feels stronger and in better condition than it's ever been," he said. "So I feel really good. And technically, I'm getting better and better and focusing on the right things in practice."
Snyder has been solid in the years since Tokyo, winning a world championship in 2022 and claiming bronze at the 2023 worlds.
He won't have an easy path back to the top of the podium. He may have to contend with 21-year-old Akhmed Tazhudinov of Bahrain, who defeated him 10-0 on his way to a world championship in 2023.
Snyder said the 6-foot 2 Tazhudinov has exceptional reach and is a technically sound defensive wrestler who excels at taking advantage of his opponents' mistakes.
"He just wrestles in a lot of weird positions and scrambles well," Snyder said. "He's able to think while he's on the mat and make adjustments."
U.S. men's freestyle coach Bill Zadick said Snyder is at his best when challenged.
"I think Kyle Snyder is the type of guy that thrives at that opportunity and that challenge," Zadick said. "He wants to be the guy that has the toughest road, the greatest competition. And he wants to be the guy. He likes to test himself. He likes to know where it's at."
One challenger who won't be there is Abdulrashid Sadulaev, who beat Snyder for the gold in Tokyo. Sadulaev competed there as part of the Russian Olympic Committee. The International Olympic Committee did not include Sadulaev on its list of eligible athletes from Russia and Belarus for the Paris Game. He had been barred from Olympic qualifiers in April by United World Wrestling, the sport's governing body, for his support of the Ukraine-Russia war.
Snyder believes he will be prepared, regardless of the opponent. He said he became a dominant wrestler because he challenged the best in practice along the way.
"Ever since I was a kid, I always thought I was going to win in everything I ever did," he said. "I don't know why I felt that way. I wrestled people that were older, better and stronger and bigger, and they kicked my butt. And then the next time we wrestle, I'd think I'd win. And then they kicked my butt. And we did that for a long time, and eventually I'd catch up to them."
Snyder adds a high level of intelligence to exceptional physical tools and his willingness to be tested. Zadick said that even when Snyder was a teenager, he was "like a 30-year-old pro, 28-year-old pro, trapped in a 17-year-old body."
"He's really sharp, really smart," Zadick said. "I think he's thinking in an innovative way and adding new things to his style and being creative. And so, I'm excited for him. He just loves that. He loves what he does. And, he's just full of passion. And that's exciting. And I think it bodes well for anybody that has that kind of drive and fire inside them."
Now, Snyder is the guy up-and-comers learn from. Heavyweight Mason Parris is making his Olympic debut, and he already has latched onto Snyder to help him prepare.
"He's a guy I've always looked up to growing up, and it's awesome that I'm able to pick his brain and learn a lot of stuff from him — a guy that is a veteran like him," Parris said. "He's an awesome dude, and I'm grateful I could train with him sometimes and learn from him."