For decades, the scientific community has been trying to reconcile abundant evidence for fluvialactivity on Noachian and early Hesperian Mars with the faint young Sun and reasonableconstraints on ancient atmospheric pressure and composition. Recently, the investigation of H2-CO2 collision-induced absorption has opened up a new avenue to warm Noachian Mars. We usethe ROCKE-3D global climate model to simulate plausible states of the ancient Martian climatewith this absorptive warming and reasonable constraints on surface paleopressure. We find that1.5-2 bar CO2-dominated atmospheres with ≥3% H2 can produce global mean surfacetemperatures above freezing, while also providing sufficient warming to avoid surfaceatmospheric CO2 condensation at 0°-45° obliquity. Simulations conducted with both moderntopography and a paleotopography, before Tharsis formed, highlight the importance of Tharsis asa cold trap for water on the planet. Additionally, we find that low obliquity (modern and 0°) ismore conducive to rainfall over valley network locations than high (45°) obliquity. PLAIN LANGUAGE SUMMARY Much evidence tells us that ancient Mars had liquid water on its surface. But reconciling thatwith the fainter young Sun and reasonable constraints on Mars' early atmosphere is challenging.We use a 3D global climate model with an atmosphere containing some amount of hydrogen (apossible greenhouse gas) to study Mars' early hydrological cycle and compare it to the geologicalevidence of surface liquid water billions of years ago. We find that hydrogen and carbon dioxidetogether in an atmosphere twice as thick as modern Earth can warm early Mars above thefreezing point of water and that a low axial tilt produces rainfall patterns that best match thegeologic evidence