Creative arts programs have potential for promoting psychological well-being amongst young people. The present research used a mixed-methods approach to address the mechanisms involved in the well-being of marginalized young people engaged in creative arts participation, based on self-determination theory. A preliminary quantitative analysis investigated the levels of basic needs satisfaction (BNS) that 42 young people reported experiencing at home, at school, and at a youth theater organization. Young people reported the highest level of BNS at the theater, and there was a marginally significant trend suggesting this had a positive association with well-being, over and above the effects of BNS at home and school. Nonetheless, Bayesian factor indicated more data is required to confirm this observation. Subsequently, an in-depth qualitative analysis was undertaken with semi-structured interviews with three young people as well as with their parents and schoolteachers. Thematic analysis highlighted the ways satisfaction of autonomy (through empowerment), relatedness (through the establishment of group membership), and competence (through creating a safe space for young people to be heard) allowed the young people to develop positive future aspirations. Study implications and directions for further work are explored in relation to the way that creative arts participation enables young people to explore possible goals and give them an understanding of what they can achieve.