The combination of radio-frequency (RF) communication and underwater optical wireless communication (UOWC) plays a vital role in the underwater Internet of Things (UIoT). This correspondence proposes a dual-hop hybrid satellite underwater system that exploits non-orthogonal multiple access (NOMA) as a spectrum-efficient access technique. The RF link from the satellite to the relay on an oil platform is presumptively subject to a Shadowed-Rician (SR) fading, while the UOWC channels from the relay to the underwater destinations are suggested to follow Exponential-Generalized Gamma (EGG) distributions. The reliability of the system is characterized in terms of both underwater destinations and system outage probabilities (OPs). We derive new closed-form expressions for the OPs under imperfect successive interference cancellation (SIC) conditions. Furthermore, the asymptotic OP and the diversity order (DO) are obtained to learn more about the system’s performance. The results are verified through an extensive representative Monte-Carlo simulation. Also, we investigate the performance against the turbulence of the salty water, air bubbles level (BL), temperature gradients (TG), shadowing parameters, and satellite pointing errors due to satellite motion, even if the beam is pointed at the center of the directive antenna relay, the beam will randomly oscillate. Finally, we contrast our approach with the conventional orthogonal multiple access (OMA) scheme to demonstrate its superiority.