Emerging as a prominent area of focus in energy conversion and storage technologies, the development of highly active metal-based single-atom catalysts (SACs) holds great significance in searching alternatives to replace precious metals toward the efficient, stable, and low-cost hydrogen evolution reaction (HER), as well as the oxygen evolution reaction (OER) and the oxygen reduction reaction (ORR). Combining the tremendous tunability of ligand and coordination environment with rich metal-based electrocatalysts can create breakthrough opportunities for achieving both high stability and activity. Herein, we propose a novel and stable holey graphene-like carbon nitride monolayer g-C₁₆N₅ (N₄@g-C₁₆N₃) stoichiometries interestingly behaving as a natural substrate for constructing SACs ((TM-N₄)@g-C₁₆N₃), whose evenly distributed holes map rich and uniform nitrogen coordination positions with electron-rich lone pairs for anchoring transition metal (TM) atoms. Then, we employed density functional theory (DFT) calculations to systematically investigate the electrocatalytic activity of (TM-N₄)@g-C₁₆N₃ toward HER/OER/ORR, meanwhile considering the synergistic modulation of H-loading and O-coordination ((TM-N_xO_4−x)@g-C₁₆N₃-H₃, x = 0–4). Together a “four-step procedure” screening mechanism with the first-principles high-throughput calculations, we find that (Rh-N₄) and (Ir-N₂O_2-II) distributed on g-C₁₆N₃-H₃ can modulate the adsorption strength of the adsorbates, thus achieving the best HER/OER/ORR performance among 216 candidates, and the lowest overpotential of 0.098/0.3/0.46 V and 0.06/0.48/0.45 V, respectively. Additionally, the d-band center, crystal orbital Hamilton population (COHP), and molecular orbitals are used to reveal the OER/ORR activity source. Particularly, the Rh/Ir-d orbital is dramatically hybridized with the O-p orbital of the oxygenated adsorbates, so that the lone-electrons incipiently locate at the antibonding orbital pair up and populate the downward bonding orbital, allowing oxygenated intermediates to be adsorbed onto (TM-N_xO_4−x)@g-C₁₆N₃-H₃ appropriately.