In this paper we present our project that aims at determining accurate distances and proper motions for the Y brown dwarf population using the Hubble Space Telescope. We validate the program with our first results, using a single new epoch of observations of the Y0pec dwarf WISE J163940.83\(-\)684738.6. These new data allowed us to refine its proper motion and improve the accuracy of its parallax by a factor of three compared to previous determinations, now constrained to \(\varpi = 211.11 \pm 0.56\) mas. This newly derived absolute parallax corresponds to a distance of \(4.737 \pm 0.013\) pc, an exquisite and unprecedented precision for faint ultracool Y dwarfs.