Artificial intelligence (AI)-enabled systems are increasingly governing access to youth services, yet empirical research remains limited on how young service users experience and evaluate AI-mediated service delivery. Based on procedural justice and institutional trust theory, the present research formulates and pilots a sequential institutional framework between AI-enabled service experience (AISE), algorithmic legitimacy (ALG), trust in AI-supported service systems (TIA), psychological well-being (PWB), and service satisfaction (SS). The respondents included youth service users (N = 418) in Pakistan who stated that they had previously used AI-supported services in education, health, and social welfare or community-based situations. To test the hypothesized relationships, structural equation modeling (SEM) was used and supplemented by importance-performance map analysis to examine the allocation of explanatory influence throughout the sequential model. TIA emerged as the most proximal and influential predictor of both PWB and SS, while ALG operated as a critical upstream mechanism shaping trust. Sequential mediation analyses further show that youth outcomes are influenced less by exposure to AI systems per se and more by evaluative judgments concerning the legitimacy and trustworthiness of AI-supported service processes. By centering youth service users and conceptualizing AI as an institutionalized component of service delivery, this study advances research on algorithmic governance in youth services and offers insights for ethically and accountably deploying AI-assisted systems to support positive youth outcomes.