The aim of this work is to obtain high-resolution values of sea surface salinity (SSS) and temperature (SST) in the global ocean by using raw satellite data (i.e., without any band data pre-processing or atmospheric correction). Sentinel-2 Level 1-C Top of Atmosphere (TOA) reflectance data is used to obtain accurate SSS and SST information. A deep neural network is built to link the band information with in situ data from different buoys, vessels, drifters, and other platforms around the world. The neural network used in this paper includes shortcuts, providing an improved performance compared with the equivalent feed-forward architecture. The in situ information used as input for the network has been obtained from the Copernicus Marine In situ Service. Sentinel-2 platform-centred band data has been processed using Google Earth Engine in areas of 100 m × 100 m. Accurate salinity values are estimated for the first time independently of temperature. Salinity results rely only on direct satellite observations, although it presented a clear dependency on temperature ranges. Results show the neural network has good interpolation and extrapolation capabilities. Test results present correlation coefficients of 82% and 84% for salinity and temperature, respectively. The most common error for both SST and SSS is 0.4 °C and 0.4 PSU. The sensitivity analysis shows that outliers are present in areas where the number of observations is very low. The network is finally applied over a complete Sentinel-2 tile, presenting sensible patterns for river-sea interaction, as well as seasonal variations. The methodology presented here is relevant for detailed coastal and oceanographic applications, reducing the time for data pre-processing, and it is applicable to a wide range of satellites, as the information is directly obtained from TOA data.