Forest damage has become more frequent in Europe in the last decades, and remote sensing offers a powerful tool for monitoring them rapidly and cost-effectively. A novel approach was developed to utilize high-resolution ESA Sentinel-2 satellite imagery and Google Earth Engine cloud computing. The processing, analysing, and visualization of vegetation and water index (NDVI, NDVIch, Z NDVI, EVI, NDWI) maps and charts derived from satellite images took place in the cloud to ensure the detection of forest disturbances in the Hungarian study site for the period 2017-2020. The index maps were classified to reveal forest disturbances, and the cloud-based method successfully showed drought and frost damage in the oak-dominated Nagyerdő forest of Debrecen. Differences in the reaction to damage between tree species were visible in the index values, therefore a Random Forest Machine Learning classifier was applied to show the spatial distribution of dominant species. Accuracy assessment was accomplished with confusion matrices that compared classified index maps to field-surveyed data, demonstrating 71% Total Accuracy for forest damage and 76% for tree species. Based on the results of this study and the resilience of Google Earth Engine, the presented method has the potential to be extended to monitor the entire Hungary.