The fundamental nature of dark matter (DM) so far eludes direct detection experiments, but it has left its imprint in the cosmic large-scale structure. Extracting this information requires artificial intelligence (AI) methods that solve how to compare complex, heterogeneous data with computationally-expensive, physically-accurate models. I will review a multi-scale, multi-epoch test of the nature of DM leveraging these AI techniques (emulators, simulation-based inference, active learning) to combine observations of the cosmic microwave background, galaxy clustering (redshift z < 2), the Lyman-alpha forest (2 < z < 5) and the high-redshift (z > 5) galaxy UV luminosity function from the Hubble and Webb Space Telescopes. I will show that both the S_8 cosmological parameter discrepancy and a new five-sigma tension in inference of the small-scale matter power spectrum can be resolved by a contribution of ultra-light axion dark matter with particle masses ~ 10^-25 eV. I will discuss prospects for adjudicating the viability of dark matter solutions in observations of the galaxy and Milky Way sub-structure distributions in the transformative Vera Rubin Observatory.