The Riga plate is a magnetized surface that influences fluid motion and boundary layer properties. It plays an important role in heat transfer, industrial processes, and aerodynamics. This study investigates the unsteady flow of a micropolar hybrid nanofluid (MHNF) over a Riga plate. The base-fluid sodium alginate (SA) has been used in the preparation of a hybrid nanofluid (HNF) consisting of CeO2 (cerium oxide) and Al2O3 (aluminum oxide) nanoparticles (NPs). The modeled equations are transformed into a dimensionless form via similarity transformations, and the resulting equations are then numerically solved using the PCM (parametric continuation method). The influence of numerous parameters on velocity, microrotation, energy, and fluid concentration profiles is demonstrated and explained using tables and figures. Results for skin friction, energy, and mass transmission rate are also provided. Comparisons to the published data corroborate the method’s accuracy. The skin friction reduces by up to 95.1263% and 34.4699%, respectively, as the velocity slip factor and the Hartmann number are varied from 0.1 to 1.0 and 1.0 to 4.0, respectively. The energy and fluid concentration transfer rates increase by up to 21.1823% and 32.4299%, respectively, as the thermal and concentration slip parameters are varied from 0.1 to 1.4 and 0.5 to 2.0, respectively. These findings have substantial significance for a wide range of engineering applications, particularly in improving heat and mass transfer processes in industrial operations, engineering, and nanotechnology.