GNSS reflection measurements in the form of delay-Doppler maps (DDM) from the CYGNSS constellation can be used to complement soil measurements from the SMAP Mission, which has a revisit rate too slow for some hydrological/meteorological studies. The standard approach, which only considers the peak value of the DDM, is subject to a significant amount of uncertainty due to the fact that the peak value of the DDM is not only affected by soil moisture, but also complex topography, inundation, and overlying vegetation. We hypothesize that information from the entire 2D DDM could help decrease uncertainty under these conditions. The application of deep learning based techniques has the potential to extract additional information from the entire DDM, while simultaneously allowing for incorporation of additional contextual information from external datasets. This work explored the data-driven approach of convolutional neural networks (CNNs) to determine complex relationships between the reflection measurement and surface parameters, providing a mechanism to achieve improved global soil moisture estimates. A CNN was trained on CYGNSS DDMs and contextual ancillary datasets as inputs, with aligned SMAP soil moisture values as the targets. Data was aggregated into training sets, and a CNN was developed to process them. Predictions from the CNN were studied using an unbiased subset of samples, showing strong correlation with the SMAP target values. With this network, a soil moisture product was generated using DDMs from 2018 which is generally comparable to existing global soil moisture products, but shows potential advantages in spatial resolution and coverage over regions where SMAP does not perform well.