McVeigh started his professional career with the Adelaide 36ers of the National Basketball League (NBL) in 2018 and spent three seasons with the team.

[5] In 2014 and 2015, McVeigh played for the BA Centre of Excellence in the South East Australian Basketball League.

[7] After leaving college, McVeigh returned to his hometown to play for the Gold Coast Rollers in the 2018 Queensland Basketball League season.

[10] After helping the Rockets win the 2021 NBL1 Central championship,[11][12] McVeigh joined the inaugural squad of the Tasmania JackJumpers, a team entering the NBL for the first time in 2021–22.

[17] The JackJumpers went on to win the NBL championship with a 3–2 grand final series victory over Melbourne United.

[19] He was named the JackJumpers Club MVP after finishing with season averages of 17.3 points and 5.9 rebounds per game.

[23] McVeigh made his debut for the Rockets in a game against the San Antonio Spurs on 6 November and scored his first points with a three-pointer against the Oklahoma City Thunder two days later.