Next-generation megawatt-scale neutrino beams open the way to studying neutrino-nucleus scattering resorting, for the first time, to gaseous targets. This represents an opportunity to improve the knowledge of neutrino cross sections in the energy region between hundreds of MeV and a few GeV, of interest for the upcoming generation of long-baseline neutrino oscillation experiments. The challenge is to accurately track and (especially) time the particles produced in neutrino interactions in large and seamless volumes down to few-MeV energies. We propose to accomplish this through an optically-read Time Projection Chamber (TPC) filled with high-pressure argon and equipped with both tracking and timing functions. In this work, we present a detailed study of the time-tagging capabilities of such a device, based on end-to-end optical simulations that include the effect of photon propagation, photosensor response, dark-count rate and pulse reconstruction. We show that the neutrino interaction time could be reconstructed from the primary-scintillation signal with a precision in the range 1-2.5 ns (𝜎) for point-like deposits with energies down to 5 MeV, and well below 1 ns for minimum-ionizing particle tracks. A discussion on previous limitations towards such a detection technology, and how they can be realistically overcome in the near future thanks to recent developments in the field, is presented (particularly the strong scintillation yields recently reported for Ar/CF4 mixtures). The performance presented in our analysis seems to be well within reach of next-generation neutrino-oscillation experiments through the instrumentation of the proposed TPC with conventional reflective materials and a SiPM carpet behind a transparent cathode.