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We demonstrate superconducting vertical interconnect access (VIA) contacts to a monolayer of molybdenum disulfide (MoS$_2$), a layered semiconductor with highly relevant electronic and optical properties. As a contact material we use MoRe, a superconductor with a high critical magnetic field and high critical temperature. The electron transport is mostly dominated by a single superconductor/normal conductor junction with a clear superconductor gap. In addition, we find MoS$_2$ regions that are strongly coupled to the superconductor, resulting in resonant Andreev tunneling and junction dependent gap characteristics, suggesting a superconducting proximity effect. Magnetoresistance measurements show that the bandstructure and the high intrinsic carrier mobility remain intact in the bulk of the MoS$_2$. This type of VIA contact is applicable to a large variety of layered materials and superconducting contacts, opening up a path to monolayer semiconductors as a platform for superconducting hybrid devices.