Accurate damage assessment after an earthquake is crucial for effective emergency response. Using ground motion information enables rapid building damage assessment when detailed damage data are unavailable. While uncertainty in earthquake parameters plays a significant role in the accuracy of rapid estimations, it is usually treated as a constant parameter rather than as a dynamic parameter that considers the amount of ground motion data collected that evolve over time. This work investigates the impact of incorporating evolving ground motion uncertainty in ground motion estimations from US Geological Survey’s (USGS) ShakeMap on post-disaster damage assessments from two methodologies: the revised Thiel–Zsutty (TZR) model and Federal Emergency Management Agency’s (FEMA) Hazus. Using data from the 2020 Indios earthquake in Puerto Rico and the 2014 Napa earthquake, we find that changes in uncertainty in estimates of peak ground acceleration reach 65% between early and late versions of the ShakeMap. We propose a process to integrate this evolution with the two damage assessment methodologies through a Monte Carlo simulation-based approach, demonstrating that it is critical to introduce dynamic ground motion uncertainty in the damage assessment process to avoid propagating unreliable measures. Both methodologies show that resulting damage estimates can be characterized by narrower distributions, indicative of reduced uncertainty and increased precision in damage estimates. For the TZR model, an improved estimate of post-disaster loss is achieved with narrower bounds in distributions of expected high scenario loss. For Hazus, the results show potential changes in the most probable damage state with an average change of 13% in the most probable damage state. The described methodology also demonstrates how uncertainty in the resulting damage state distributions can be reduced compared with the use of the current Hazus methodology.