Global Navigation Satellite Systems (GNSS) radio occultation (RO) is one of the most vital remote sensing techniques globally and of major importance for numerical weather prediction (NWP) and climate science. However, retrieving profiles of atmospheric quantities such as temperature or humidity from GNSS observations is not straightforward and dedicated algorithms still have their limitations. One of these limitations is the need for external meteorological data in the retrieval process. Various new RO missions have led to an enormous increase in data amounts and with over 10000 globally-distributed, daily profiles, RO can be considered big data nowadays. In this study, we make use of this fact by developing a new retrieval method based on a deep learning model, which only needs RO-specific quantities as an input to produce atmospheric profiles. The model is trained on almost a full year of data from COSMIC-2 and Spire RO missions, using vertical profiles of bending angle (BA) and other RO parameters as input features and operational results from a standard retrieval algorithm as target values for supervised learning. Initial results from both internal and external validation using reanalysis and radiosonde data suggest that this method produces results with an accuracy comparable to standard algorithms, while mitigating the need for external information in the retrieval process itself. These initial results serve as a starting point for further development of data-driven models for RO, which could significantly enhance the quality of RO products utilized in, e.g., climate sciences by mitigating external biases and increasing independence from other techniques.