Surface soil moisture (SM) is a crucial variable representing the water content in soil at the topmost soil layer. Accurate data of SM are essential for various purposes, including the monitoring of drought, vegetation modeling, weather forecasting, and agriculture management. Over the past decades, microwave remote sensing has been employed to estimate SM at large scales, with the Sentinel-1 satellite mission recently offering Synthetic Aperture Radar (SAR) data and enabling to estimate SM at high spatial resolution. Machine learning (ML) techniques have further enhanced these estimations, with random forest (RF) emerging as a promising method due to its strong capabilities. However, the performance of RF in estimating SM with satellite data has not yet been thoroughly evaluated across large areas. This study presents a new RF-based model for estimating SM over Europe with SAR data from Sentinel-1, along with the climate and terrain data. The predictions from the RF model were compared against the ground measurements from the International Soil Moisture Network (ISMN), Integrated Carbon Observation System (ICOS), and official SMAP/Sentinel-1 SM products. The results demonstrated that the RF model yielded accurate predictions with a Pearson's correlation coefficient (R) of 0.847 outperforming the official SMAP/Sentinel-1 product at spatial resolutions of 1 km and 3 km, which achieved R values of 0.599 and 0.616, respectively. Additionally, the impact of vegetation cover that is represented by using multiple satellite vegetation products on the RF model was investigated. Despite a moderate correlation between backscattering coefficients and vegetation cover, no correlation was found between the RF model's errors and vegetation cover. The results suggest that the RF model and Sentinel-1 SAR data can be used to provide SM estimations at high spatial resolution, characterizing the fine-scale variations in SM, to support various applications such as precision agriculture at the small, localized scales.