Born in Bradford, West Yorkshire, England in 1984, Muj moved around as a child, his Parents settled in Derby, Derbyshire, England in the early 90's. Pursuing his passion for acting he auditioned for and was accepted into the National Youth Theatre, while still gaining experience at University. Upon graduating he won a scholarship and went on to train at the British American Drama Academy, where he played Caesar in William Shakespeare's Julius Caesar and the titular character in Shakespeare's Othello.

Furthering his skills with Stage Combat and taking on minor roles marked the beginning of his professional career. Appearing in BBC's Hustle (2004), soon after appearing as 'Skinny Mo' in Bonded by Blood (2010). His experience on this film landed him the role of 'Sheikh Ali Kharma' alongside 'Bob Hoskin (I)' in the British film Outside Bet (2012). He then went on to play the starring role of 'Saleh' in Casualty (1986) a special episode called Casualty: Under Fire. With a burning desire to do more with his career Muj briefly relocated to Toronto, Canada where he provided voice over for The History Channel's production of Miracles Decoded (2014). Upon returning to the UK, he starred in a short film Freeze Frame and later that year appeared as Haroon Latif in an episode of Citizen Khan (2012).

He then went on to appear as Doctor Collins in Songbird (2018) and was then later cast as the lovable Bilal, one of the lead characters in BBC3's new comedy series Coconut (2017). The same year he was Highly Commended by Faber & Faber for his writing on his Graphic Novel 'Maghrib.' about a Muslim superhero which was created as a counter narrative to the negative portrayal of Muslims within the media. This spurred on a desire to write more, even taking an initial idea he had for a novel to be developed into a TV Series. Along with his writing partner Harrie Hayes (Lead Actress in Horrible Histories, BBC) they produced a script which attracted the attention of a BAFTA Winning Director Declan Lowney (Alan Partridge: Alpha Papa, Idris Elba's In The Long Run). Developing the project together this past year has been a defining moment in his life and opened himself up to the world of Screen Writing. Whilst focusing on his writing, he had greatly improved and grown as an artist, returning to the very first panel of his comic to reinvigorate it with a new lease of life. He was again Highly Commended but this time for his Illustrations in the 2019 Faber & Faber Fab Prize.