An efficient combination of the data collected by multiple instruments and platforms is needed to obtain accurate 3D ocean state estimates, representing a fundamental step to describe ocean dynamics and its role in the Earth climate system and marine ecosystems. Observations can either be assimilated in ocean general circulation models or used to feed data-driven reconstructions and diagnostic models. Here we describe an innovative deep learning algorithm that projects sea surface satellite data at depth after training with sparse co-located in situ vertical profiles. The technique is based on a stacked Long Short-Term Memory neural network, coupled to a Monte-Carlo dropout approach, and is applied here to the measurements collected between 2010 and 2018 over the North Atlantic Ocean. The model provides hydrographic vertical profiles and associated uncertainties from corresponding remotely sensed surface estimates, outperforming similar reconstructions from simpler statistical algorithms and feed-forward networks.