The ability to reconstruct the three-dimensional (3D) dynamics of the ocean by an effective version of Surface Quasi-Geostrophy (eSQG) is examined. Using the fact that surface density plays an analogous role as interior potential vorticity (PV), the eSQG method consists in inverting the QG PV generated by sea-surface density only. We also make the extra assumption that sea-surface temperature (SST) anomalies fully represent surface density anomalies. This approach requires a single snapshot of SST and the setup of two parameters: the mean Brunt-Vaisala frequency and a parameter that determines the energy level at the ocean surface. The validity of this approach is tested using an Ocean General Circulation Model simulation representing the North Atlantic in winter. It is shown that the method is quite successful in reconstructing the velocity field at the ocean surface for mesoscales (between 30 and 300 km). The eSQG framework can also be applied to reconstruct subsurface fields using surface information. Results show that the reconstruction of velocities and vorticity from surface fields is reasonably good for the upper 500 m and that the success of the method mainly depends on the quality of the SST as a proxy of the density anomaly at the base of the mixed layer. This situation happens after a mixed-layer deepening period. Therefore the ideal situation for the application of this method would be after strong wind events.