The sustainable management of natural heritage is presently considered a global strategic issue. Owing to the ever-growing availability of free data and software, remote sensing (RS) techniques have been primarily used to map, analyse, and monitor natural resources for conservation purposes. The need to adopt multi-scale and multi-temporal approaches to detect different phenological aspects of different vegetation types and species has also emerged. The time-series composite image approach allows for capturing much of the spectral variability, but presents some criticalities (e.g., time-consuming research, downloading data, and the required storage space). To overcome these issues, the Google Earth engine (GEE) has been proposed, a free cloud-based computational platform that allows users to access and process remotely sensed data at petabyte scales. The application was tested in a natural protected area in Calabria (South Italy), which is particularly representative of the Mediterranean mountain forest environment. In the research, random forest (RF), support vector machine (SVM), and classification and regression tree (CART) algorithms were used to perform supervised pixel-based classification based on the use of Sentinel-2 images. A process to select the best input image (seasonal composition strategies, statistical operators, band composition, and derived vegetation indices (VIs) information) for classification was implemented. A set of accuracy indicators, including overall accuracy (OA) and multi-class F-score (Fm), were computed to assess the results of the different classifications. GEE proved to be a reliable and powerful tool for the classification process. The best results (OA = 0.88 and Fm = 0.88) were achieved using RF with the summer image composite, adding three VIs (NDVI, EVI, and NBR) to the Sentinel-2 bands. SVM and RF produced OAs of 0.83 and 0.80, respectively.