For decades the scientific community has been trying to reconcile abundant evidence for fluvial activity on Noachian and early Hesperian Mars with the faint young Sun and reasonable constraints 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 use the ROCKE-3D global climate model to simulate plausible states of the ancient Martian climate with this absorptive warming and reasonable constraints on surface paleopressure. We find that 1.5-2 bar CO2-dominated atmospheres with 3% H2 can produce global mean surface temperatures above freezing, while also providing sufficient warming to avoid surface atmospheric CO2 condensation at 0°-45° obliquity. Simulations conducted with both modern topography and a paleotopography, before Tharsis formed, highlight the importance of Tharsis as a cold trap for water on the planet. Additionally, we find that low obliquity (modern and 0°) is more conducive to rainfall over valley network locations than high (45°) obliquity.