Ground-penetrating radar (GPR) is a mature geophysical method that has gained increasing popularity in planetary science over the past decade. GPR has been utilised both for Lunar and Martian missions providing pivotal information regarding the near surface geology of Terrestrial planets. Within that context, numerous processing pipelines have been suggested to address the unique challenges present in planetary setups. These processing pipelines often require manual tuning resulting to ambiguous outputs open to non-unique interpretations. These pitfalls combined with the large number of planetary GPR data (kilometers in magnitude), highlight the necessity for automatic, objective and advanced processing and interpretation schemes. The current paper investigates the potential of deep learning for interpreting and processing GPR data. The one-shot multi-offset configuration is investigated via a coherent numerical case study, showcasing the potential of deep learning for A) reconstructing the dielectric distribution of the the near surface of Terrestrial planets, and B) filling missing or bad-quality traces. Special care was taken for the numerical data to be both realistic and challenging. Moreover, the generated synthetic data are properly labelled and made publicly available for training future data-driven pipelines and contributing towards developing pre-trained foundation models for GPR.