Abstract Satellite altimetry combined with data assimilation and optimal interpolation schemes have deeply renewed our ability to monitor sea surface dynamics. Recently, deep learning schemes have emerged as appealing solutions to address space‐time interpolation problems. However, the training of state‐of‐the‐art neural schemes on real‐world case‐studies is hindered by the sparse space‐time coverage of the sea surface of real altimetry data set. Here, we introduce an innovative approach that leverages state‐of‐the‐art ocean models to train simulation‐based neural schemes for the mapping of sea surface height and demonstrate their performance on real altimetry data sets. We analyze further how the ocean simulation data set used during the training phase impacts this performance. This experimental analysis covers both the resolution from eddy‐present configurations to eddy‐rich ones, forced simulations versus reanalyzes using data assimilation and tide‐free versus tide‐resolving simulations. Our benchmarking framework focuses on a Gulf Stream region for a realistic 5‐altimeter constellation using NEMO ocean simulations and 4DVarNet mapping schemes. All simulation‐based 4DVarNets outperform the operational observation‐driven and reanalysis products, namely DUACS and GLORYS. The more realistic the ocean simulation data set used during the training phase, the better the mapping. The best 4DVarNet mapping was trained from an eddy‐rich and tide‐free simulation data sets. It improves the resolved longitudinal scale from 151 km for DUACS and 241 km for GLORYS to 98 km and reduces the root mean square error by 23% and 61%. These results open research avenues for new synergies between ocean modeling and ocean observation using learning‐based approaches.