[3] While living in Sydney as a teenager, Muo starting playing basketball for the first time in a local park.

As he began to love the sport and realising his natural talent, Muo decided to take the game seriously, partly as a way to keep himself out of trouble.

[4] Though he received a diploma, Muo did not qualify through the NCAA Clearinghouse and instead attended Quinnipiac University as an international student for one year.

[7] In 2011, Muo once again moved colleges, this time landing at Charleston Southern University and joined the Buccaneers men's basketball team.

[6] On 7 June 2013, Muo signed a three-year deal with the Perth Wildcats of the National Basketball League.

[8][9] However, on 13 August 2013, he suffered a tear to his left Achilles tendon during the second official training session of the team's pre-season schedule.

[12][13] He attended every training session throughout the 2013–14 season and remained a big part of the Wildcats playing group, and watched on as his team won the NBL championship in April 2014.

[14][15] On 16 May 2014, Muo joined the East Perth Eagles of the State Basketball League for the rest of the 2014 season.

[18] On 5 September 2014, Muo took to the court for the first time in a Wildcats singlet, playing in a pre-season game against the SBL All-Stars.

He showed signs of being able to make an impact at NBL level, finishing with seven points in 18 minutes of court time in Perth's 98–59 win.

[20][21] He continued to train with the team while exploring opportunities elsewhere; the Wollongong Hawks were reportedly on the radar at the time of his release.

[22] Days after the Wildcats' season-opening home loss to the New Zealand Breakers, back-up forward Greg Hire sustained a calf injury that ruled him out for six weeks.

[24][25] He went on to make his long-awaited NBL debut on 17 October 2014 in the Wildcats' 69–59 win over the Wollongong Hawks, recording one turnover in just under two minutes of action.

[33] On 24 March 2015, Muo signed with the Goldfields Giants for the rest of the 2015 State Basketball League season.

[34][35][36] Four days later, he made his debut for the Giants, recording 31 points, 17 rebounds, four assists and three steals in a 111–101 loss to the Joondalup Wolves.

[40] The Giants went on to sweep the Geraldton Buccaneers in the quarter-finals,[41] before losing in straight sets to the South West Slammers in the semi-finals.

[43] He made his debut for the Spartans in the team's season opener on 1 April, recording game highs of 25 points and 11 rebounds in a 73–55 loss to the Geelong Supercats.

[46] On 30 July, he had his second-best scoring performance of the season with 31 points in a 93–81 win over the Albury Wodonga Bandits.

[55] He made his debut for the Chargers in their season opener on 25 March, recording 28 points and 10 rebounds in a 98–41 win over the North-West Tasmania Thunder.

On 18 August, the Chargers were knocked out of the playoffs with a 105–98 loss to the Dandenong Rangers in the South Conference Preliminary Final,[61] despite an 18-point effort from Muo.

They went on to reach the SEABL Grand Final, where they defeated the Nunawading Spectres 72–58 behind Muo's MVP performance of 20 points and 14 rebounds.

[104][105] In July 2016, Muo was selected to represent South Sudan in the first World Indigenous Basketball Challenge.

Muo helped South Sudan reach the championship game, where they defeated Lords of the Plains 98–91 to complete a 4–0 run.

[107][108] In March 2017, Muo represented South Sudan in their debut at the AfroBasket Zone Five qualifiers in Cairo, Egypt.

[109] At the FIBA AfroBasket 2021, Muo averaged 10.8 points, 5.0 rebounds and 1.3 steals in four games for South Sudan.