For a Josephson junction array with hybrid superconductor/metal/ superconductor junctions, a quantum phase transition from a superconducting to a two-dimensional (2D) metallic ground state is predicted to occur on increasing the junction normal state resistance. Owing to its surface-exposed 2D electron gas and its gate-tunable charge carrier density, graphene coupled to superconductors is the ideal platform to study such phase transitions between ground states. Here, we show that decorating graphene with a sparse and regular array of superconducting discs enables the continuous gate-tuning of the quantum superconductor-to-metal transition of the Josephson junction array into a zero-temperature metallic state. The suppression of proximity-induced superconductivity is a direct consequence of the emergence of quantum fluctuations of the superconducting phase of the discs. Under perpendicular magnetic fields, the competition between quantum fluctuations and disorder is responsible for the resilience of superconductivity at the lowest temperatures, supporting a glassy state that persists above the upper critical field. We provide the entire phase diagram of the disorder and magnetic-field-tuned transition to reveal the role of quantum phase fluctuations in 2D superconducting systems.