The recent devastating 2023 Türkiye earthquakes underscored the urgent need for an early estimate of quantitative losses following destructive seismic events. This study aims to propose and validate a Rapid Damage Assessment (RDA) methodology based solely on open data and tools, easily and readily available globally immediately after a seismic event. In this context, the 2023 Türkiye earthquakes are used as a case study. For the application of the proposed methodology there are two prerequisites: (1) ground shaking data, herein obtained from the US Geological Survey (USGS) ShakeMap system, and (2) a predictive seismic risk model appropriate for the area of interest, consisting of an exposure and a vulnerability model, derived from the 2020 European Seismic Risk Model (ESRM20). Scenario-type analyses for the two major events, the M7.8 - Pazarcik and the M7.5 – Elbistan earthquake, are performed, and the results are compared with the officially reported damages. The main goal is to assess the accuracy of RDA immediately after an earthquake, and whether and to what extent the RDA results can be improved as the USGS ShakeMaps are updated with the incorporation of additional data, and with disaggregation of the exposure model at a finer resolution. The results indicate that the exposure model's disaggregation reduces the damage estimates' standard deviation. At the same time, the effect of the ShakeMap version is minimized when the complete fault rupture is incorporated into the model. The estimated damages are in good agreement with the officially announced data at large scale, which corroborates the proposed methodology, as well as the adopted components of ESRM20.