We present the Hubble Missing Globular Cluster Survey (MGCS), a Hubble Space Telescope Treasury Program dedicated to the observation of all kinematically confirmed Milky Way globular clusters that missed previous Hubble imaging. After introducing the aims of the programme and describing its target clusters, we showcase the first results of the survey. These are related to two clusters, one located at the edge of the Milky Way bulge and observed in optical bands, namely ESO452-11, and one located in the Galactic disc observed in the near-IR, namely 2MASS-GC01. For both clusters, the deep colour-magnitude diagrams obtained from the MGCS observations reach several magnitudes below their main-sequence turn-off and thus enable the first precise estimate of their age. By using the methods developed in the Cluster Ages to Reconstruct the Milky Way Assembly (CARMA) project, we find ESO452-11 to be an old metal-intermediate globular cluster, with [M/H]≃‑0.80‑0.11+0.08 and an age of t=13.59‑0.69+0.48 Gyr. Its location on the agemetallicity relation makes it consistent with an in situ origin, in agreement with its dynamical properties. On the other hand, the results for 2MASS-GC01 highlight it as a young metal-intermediate cluster, with an age of t=7.22‑1.11+0.93Gyr at [M/H]=‑0.73‑0.06+0.06. Despite the large associated uncertainty, our age estimate for this extremely extincted cluster indicates it to be either the youngest globular cluster known to date or a massive and compact open cluster, which is consistent with its almost circular, disc-like orbit.