The primary processes that occur following direct irradiation of bio-macromolecules by ionizing radiation determine the multiscale responses that lead to biomolecular lesions. The so-called physical stage loosely describes processes of energy deposition and molecular ionization/excitation but remains largely elusive. We propose a new approach based on first principles density functional theory to simulate energy deposition in large and heterogeneous biomolecules by high-energy-transfer particles. Unlike traditional Monte Carlo approaches, our methodology does not rely on pre-parametrized sets of cross-sections, but captures excitation, ionization and low energy electron emission at the heart of complex biostructures. It furthermore gives access to valuable insights on ultrafast charge and hole dynamics on the femtosecond time scale. With this new tool, we reveal the mechanisms of ionization by swift ions in microscopic DNA models and solvated DNA comprising almost 750 atoms treated at the DFT level of description. We reveal a so-called ebb-and-flow ionization mechanism in which polarization of the irradiated moieties appears as a key feature. We also investigate where secondary electrons produced by irradiation localize on chemical moieties composing DNA. We compare irradiation of solvated DNA by light (H+, and He2+) vs. heavier (C6+) ions, highlighting the much higher probability of double ionization with the latter. Our methodology constitutes a stepping stone towards a greater understanding of the chemical stage and more generally towards the multiscale modelling of radiation damage in biology using first principles.