Synthetic aperture radar (SAR) interferometry (InSAR) is performed using repeat-pass geometry. InSAR technique is used to estimate the topographic reconstruction of the earth surface. The main problem of the range-Doppler focusing technique is the nature of the two-dimensional SAR result, affected by the layover indetermination. In order to resolve this problem, a minimum of two sensor acquisitions, separated by a baseline and extended in the cross-slant-range, are needed. However, given its multi-temporal nature, these techniques are vulnerable to atmosphere and Earth environment parameters variation in addition to physical platform instabilities. Furthermore, either two radars are needed or an interferometric cycle is required (that spans from days to weeks), which makes real time DEM estimation impossible. In this work, the authors propose a novel experimental alternative to the InSAR method that uses single-pass acquisitions, using a data driven approach implemented by Deep Neural Networks. We propose a fully Convolutional Neural Network (CNN) Encoder-Decoder architecture, training it on radar images in order to estimate DEMs from single pass image acquisitions. Our results on a set of Sentinel images show that this method is able to learn to some extent the statistical properties of the DEM. The results of this exploratory analysis are encouraging and open the way to the solution of single-pass DEM estimation problem with data driven approaches.