Cross-section predictions are crucial for the success of long-baseline neutrino experiments, but they suffer from significant theoretical uncertainties. Given the promise of future near detector data, one certainly expects and needs to utilize such data to improve cross-section modeling. We want to explore this idea to its fullest extent by constructing a cross-section model that is nearly devoid of theoretical assumptions and that maximizes the information extracted from the data. We propose using machine learning techniques to train a systematically improvable model of neutrino-nucleus scattering, employing DUNE near detector data. We demonstrate, using simulated data, that such a trained model can subsequently be used to perform an oscillation analysis. This introduces a complementary approach that could be extended to realistic experimental analyses and could further be used to validate and improve microscopic models of neutrino-nucleus cross sections.