The advent of satellite altimetry datasets of sea surface height (SSH) is a major advance in oceanography and other Earth system sciences. However, while the along-track data coverage is dense, the relatively poor resolution between tracks poses a challenge to the reconstruction of those processes such as mesoscale and submesoscale eddies. This study proposes a machine learning algorithm based on a causal inference tool, i.e., the Liang–Kleeman information flow (L-K IF) analysis, to address the challenge. For a region in the South China Sea where eddies frequently appear but unobserved, it is shown that the algorithm can reconstruct the desired mesoscale eddies in a remarkably successful way in geometry, orientation, strength, etc., while with the objective analysis interpolation or the traditional neural network technique, the results are not satisfactory. This study provides prospects for developing the next generation of SSH products with the available altimetry data.