[2] He attended Stevenson High School in Lincolnshire, Illinois, before enrolling at the University of Michigan to pursue gymnastics.

In August 2017, he competed at the 2017 U.S. National Gymnastics Championships in the junior division, where he won a silver medal in the all-around and on still rings and parallel bars.

[7] In August 2019, he competed at the 2019 U.S. National Gymnastics Championships, where he won bronze on horizontal bar, and compiled a score of 159.850 to place 13th.

[8] Following his performance at the competition, he was named to the United States men's national junior gymnastics team.

[9] In February 2020, Juda competed at the 2020 Winter Cup, where he won bronze on horizontal bars, tied for fifth on floor exercise, and eighth in all-around (81.650).

[10] Following his outstanding performance at the Winter Cup, he was named to the United States men's national gymnastics team.

[18][19] During the 2021 NCAA season, he captured thirteen event titles and was the top-ranked all-around gymnast in the country, with a national qualifying average of 86.167.

1 in the Big Ten on parallel bars (14.617), and second in the league on floor exercise (14.533), still rings (14.300) and pommel horse (14.250).

[26] In March 2022, Juda competed at the Cairo World Cup, where he won silver on the floor exercise and horizontal bar.

[27] During the 2022 NCAA season, he won eleven event titles and was named Big Ten Gymnast of the Week twice.

[30] During the 2022 NCAA Men's Gymnastics Championship, Juda won the all-around with an 85.298, and vault individual titles, and helped Michigan place third in the team competition with a season-best 414.490.

[34] The following day he was named to the team to compete at the upcoming World Championships alongside Asher Hong, Khoi Young, Yul Moldauer, Fred Richard, and alternate Colt Walker.

During the team final he contributed scores on rings, vault, and horizontal bar toward the USA's third-place finish.

[43] Following the 2024 Summer Olympics, Juda became the chief revenue and brand officer at GymnastX, a gymnastics apparel company.