Screening unique structures are critical to developing efficient photocatalytic materials for solar-to-hydrogen conversion via hydrogen evolution reaction (HER). Here, we demonstrate the discovery of two-dimensional Ga₂S₃ monolayers as efficient photocatalysts. By performing screening over 30 generations of 30 populations using the universal structure predictor evolutionary xtallography method, accompanied by accessing the stabilities and matching with photocatalytic conditions for overall water splitting, we identify 7 preferable configurations from 1038 Ga₂S₃ monolayers. The bandgaps and overpotentials of the band edges of these monolayers are used to justify the hydrogen and oxygen evolution reactions and evaluate the solar-to-hydrogen conversion efficiencies, and alterations of Gibbs free energy in HERs and oxygen evolution reactions (OERs) are calculated to validate the thermodynamics feasibility. The maximum efficiency of 17.71% is observed for one Ga₂S₃ monolayer with the P1 space group, and higher efficiency of 19.58% can be boosted with a suitable strain. Moreover, the moderate alterations of the Gibbs free energy assure the HERs are achievable in thermodynamics and the OERs can proceed spontaneously in thermodynamics on the GS-1, 4, 6, and 7 monolayers, although those on the GS-2, 3, 5 monolayers need small external energies. These results indicate that the screened Ga₂S₃ monolayers can be used as promising candidates for sunlight photocatalytic overall water splitting to manufacture hydrogen.