College & Youth Nelson attended and played soccer at
Seven Lakes High School in
Katy, Texas. He helped them win a district championship and was named first team all-state. He also helped his youth club, Albion Hurricanes FC, win 2 state championships. Nelson played
college soccer at
Southern Methodist University between 2014 and 2017, including spending a year as a redshirt in 2013. While with the
Mustangs, Nelson made 76 appearances and contributed 27 shutouts. He was named
American Athletic Conference Goalkeeper of the Year in 2014, 2015, and 2017 and was first team all-conference in 2014, 2015, and 2017 During his time in college, Nelson also spent time with
Premier Development League side
OKC Energy U23 during their 2016 season.
Professional Nelson was drafted in the first round, 20th overall, in the
2018 MLS SuperDraft by the
Houston Dynamo on January 19, 2018. Nelson signed with Houston on February 20, 2018. He spent the 2018 season on loan with the Dynamo
USL affiliate
Rio Grande Valley FC. On June 23, 2018, he made his Toros debut and kept a clean sheet against
Phoenix Rising. On the season, Nelson made 7 appearances and kept 3 clean sheets. Nelson spent most of 2019 with the Toros again, making 8 appearances and keeping 1 clean sheet. However, he did make his Dynamo debut on June 18 in a 3–2 defeat to
Minnesota United in the
US Open Cup. In 2020, Nelson stayed with the first team for the whole season, but he failed to appear in any games. He did make the match day squad on 3 occasions. On August 28, 2021, with starting goalkeeper
Marko Marić out with a leg injury, Nelson made his MLS debut in a 2–1 loss to Minnesota United. The game was the first of 10 consecutive starts for Nelson. He was named to the MLS Team of the Week for his performance on September 15 in a 1–1 draw with the
LA Galaxy. After Marić returned from injury, Nelson started one of the final 3 games of the season. Nelson ended the season with 11 appearances and 2 clean sheets. Nelson made 5 first team appearances during the 2022 season, 2 in the league and 3 in the Open Cup. He also made 5 appearances for
Houston Dynamo 2. On February 16, 2023, Nelson was waived by the Dynamo. He subsequently signed with
USL Championship side
FC Tulsa on March 3, 2023. == Honors ==