In the pursuit of sustainable clean energy sources, the hydrogen evolution reaction (HER) has attained significant interest from the scientific community. Single-atom catalysts (SACs) are among the most promising candidates for future electrocatalysis because they possess high thermal stability, effective electrical conductivity, and excellent percentage atom utilization. In the present study, the applicability of late first-row transition metals (Fe-Zn) decorated on the magnesium oxide nanocage (TM@Mg12O12) as SACs for the HER has been studied, via density functional theory. The late first-row transition metals have been chosen as they have high abundance and are relatively low-cost. Among the studied systems, results show that the Fe@Mg12O12 SAC is the best candidate for catalyzing the HER reaction as it exhibits the lowest activation barrier for HER. Moreover, Fe@Mg12O12 shows high stability (Eint = −1.64 eV), which is essential in designing SACs to prevent aggregation of the metal. Furthermore, the results of the electronic properties’ analysis showed that the HOMO-LUMO gap of the nanocage is decreased significantly upon doping of Fe (from 4.81 to 2.28 eV), indicating an increase in the conductivity of the system. This study highlights the potential application of the TM@nanocage SAC systems as effective HER catalysts.