(1) Background: Simulation of soil water infiltration process and analysis of its influencing factors are important for water resources management. (2) Methods: In this study, the relative contributions of the soil water retention characteristics (SWRC) estimation, initial water content, and constant pressure head at upper boundary to the cumulative infiltration under various soil conditions were quantified based on the 1-D Richards’ equation and 900 scenarios. Scenario simulations were performed for two SWRC estimation methods (Jensen method and Rosetta); three different initial water contents (0.15, 0.20, and 0.25 cm³/cm³); five different constant pressure heads (0.5, 1, 2, 4, and 8 cm); and thirty soil samples with varying texture and bulk density. (3) Results: Rosetta representing the drying branch of the SWRC yielded higher simulated cumulative infiltration compared with the Jensen method representing the wetting branch of the SWRC. However, the Jensen method–predicted cumulative infiltration fluxes matched well with the measured values with a low RMSE of 0.80 cm. (4) Conclusions: The relative contribution of the SWRC estimation method to cumulative infiltration (19.1–72.2%) was compared to that of constant pressure head (14.0–65.5%), and generally greater than that of initial water content (2.2–29.9%). Findings of this study have practical significance for investigating the transport of water, nutrients, and contaminants in the unsaturated zone.