Soil moisture is a key environmental variable, important to, e.g., farmers, meteorologists, and disaster management units. Here, we present a method to retrieve surface soil moisture (SSM) from the Sentinel-1 (S-1) satellites, which carry C-band Synthetic Aperture Radar (CSAR) sensors that provide the richest freely available SAR data source so far, unprecedented in accuracy and coverage. Our SSM retrieval method, adapting well-established change detection algorithms, builds the first globally deployable soil moisture observation data set with 1-km resolution. This paper provides an algorithm formulation to be operated in data cube architectures and high-performance computing environments. It includes the novel dynamic Gaussian upscaling method for spatial upscaling of SAR imagery, harnessing its field-scale information and successfully mitigating effects from the SAR's high signal complexity. Also, a new regression-based approach for estimating the radar slope is defined, coping with Sentinel-1's inhomogeneity in spatial coverage. We employ the S-1 SSM algorithm on a 3-year S-1 data cube over Italy, obtaining a consistent set of model parameters and product masks, unperturbed by coverage discontinuities. An evaluation of therefrom generated S-1 SSM data, involving a 1-km soil water balance model over Umbria, yields high agreement over plains and agricultural areas, with low agreement over forests and strong topography. While positive biases during the growing season are detected, the excellent capability to capture small-scale soil moisture changes as from rainfall or irrigation is evident. The S-1 SSM is currently in preparation toward operational product dissemination in the Copernicus Global Land Service.