As climate changes, changes in Antarctic Ice Sheet (AIS) snow accumulation can modulate the rate of global sea level rise. An ice-core-based reconstruction revealed that a cumulative mass gain due to increased snow accumulation mitigated global sea level by ~10 mm during the 20th Century (Medley and Thomas, 2019). Here we attribute this trend and project it forward by employing a suite of single-forcing, all-forcing and nudged ensembles from a well-evaluated Earth System Model. Rising concentrations of greenhouse gasses have driven the snow accumulation increase, while anthropogenic aerosols and observed tropical Pacific sea surface temperature anomalies have played dampening roles. Together, these factors drive global- and Antarctic- mean temperatures, the main physical controls on snowfall changes, and can quantitatively explain the historical sea level mitigation. We also examine the modeled and observed spatial patterns of snow accumulation trends, and the roles of strengthening westerly winds and external forcings in shaping these patterns.