Land cover (LC) is a crucial parameter for studying environmental phenomena. Cutting-edge technology such as remote sensing (RS) and cloud computing have made LC change mapping efficient. In this study, the LC of Rupandehi District of Nepal were mapped using Landsat imagery and Random Forest (RF) classifier from 2005 to 2020 using Google Earth Engine (GEE) platform. GEE eases the way in extracting, analyzing, and performing different operations for the earth’s observed data. Land cover classification, Centre of gravity (CoG), and their trajectories for all LC classes: agriculture, built-up, water, forest, and barren area were extracted with five-year intervals, along with their Ecosystem service values (ESV) to understand the load on the ecosystem. We also discussed the aspects and problems of the spatiotemporal analysis of developing regions. It was observed that the built-up areas had been increasing over the years and more centered in between the two major cities. Other agriculture, water, and forest classes had been subjected to fluctuations with barren land in the decreasing trend. This alteration in the area of the LC classes also resulted in varying ESVs for individual land cover and total values for the years. The accuracy for the RF classifier was under substantial agreement for such fragmented LCs. Using LC, CoG, and ESV, the paper discusses the need for spatiotemporal analysis studies in Nepal to overcome the current limitations and later expansion to other regions. Studies such as these help in implementing proper plans and strategies by district administration offices and local governmental bodies to stop the exploitation of resources.