Accurate and real-time land use/land cover (LULC) maps are important to provide precise information for dynamic monitoring, planning, and management of the Earth. With the advent of cloud computing platforms, time series feature extraction techniques, and machine learning classifiers, new opportunities are arising in more accurate and large-scale LULC mapping. In this study, we aimed at finding out how two composition methods and spectral–temporal metrics extracted from satellite time series can affect the ability of a machine learning classifier to produce accurate LULC maps. We used the Google Earth Engine (GEE) cloud computing platform to create cloud-free Sentinel-2 (S-2) and Landsat-8 (L-8) time series over the Tehran Province (Iran) as of 2020. Two composition methods, namely, seasonal composites and percentiles metrics, were used to define four datasets based on satellite time series, vegetation indices, and topographic layers. The random forest classifier was used in LULC classification and for identifying the most important variables. Accuracy assessment results showed that the S-2 outperformed the L-8 spectral–temporal metrics at the overall and class level. Moreover, the comparison of composition methods indicated that seasonal composites outperformed percentile metrics in both S-2 and L-8 time series. At the class level, the improved performance of seasonal composites was related to their ability to provide better information about the phenological variation of different LULC classes. Finally, we conclude that this methodology can produce LULC maps based on cloud computing GEE in an accurate and fast way and can be used in large-scale LULC mapping.