Hydrogen energy, characterized by its zero carbon emissions and high energy density, has emerged as a pivotal renewable and clean energy source amid the global transition toward a low-carbon energy structure. Electrocatalytic water splitting for hydrogen production not only enhances hydrogen generation efficiency but also reduces carbon emissions, offering a promising pathway for large-scale green hydrogen production. In recent years, single-atom catalysts (SACs) have become key catalytic materials for water electrolysis due to their high atom utilization efficiency, tunable electronic structures, and superior catalytic performance. In this study, density functional theory (DFT) combined with machine learning was employed to systematically investigate the hydrogen evolution reaction (HER) performance of a novel two-dimensional iron-based SAC, denoted as Fe-N₄-2N, supported on a carbon substrate with dual nitrogen coordination. Specifically, a support vector regression (SVR) model was applied to identify the dominant descriptors governing △G_*H across five Fe-N₄-2X (X = C, N, S, P, B) configurations. The results demonstrate that Fe-N₄-2N exhibits good structural stability, where elastic constant analysis and ab initio molecular dynamics (AIMD) simulations at 300 K confirm that Fe-N₄-2N maintains structural integrity throughout the catalytic process. Its hydrogen adsorption energy difference (△G_*H ≈ 0.06 eV) is much closer to the thermoneutral value (0 eV) than that of Fe-N₄-C (△G_*H ≈ 0.24 eV), indicating its superior catalytic potential for water-splitting hydrogen production. Electronic structure analysis together with machine learning results further reveal that the charge transfer of the Fe center serves as the dominant descriptor governing △G_*H in Fe-based catalysts, confirming that coordination environment induced electronic structure modulation plays a crucial role in optimizing the adsorption/desorption balance during HER. Therefore, dual nitrogen coordination effectively enhances the HER activity of Fe-N₄-C-based catalysts. This work suggests that deliberate modulation of the local coordination environment around Fe-center single atoms represents a broadly applicable strategy for developing high-performance single-atom electrocatalysts beyond the Fe-N₄ system.