The superconducting proximity effect has recently attracted a renewed interest as the basis of topologically nontrivial states in materials with a large spin-orbit interaction, with protected boundary states useful for quantum information technologies. However, spectroscopy of these states is challenging because of the limited control of conventional tunnel barriers. Here we report electronic spectroscopy measurements of the proximity gap in a semiconducting indium arsenide nanowire segment coupled to a superconductor, using quantum dots formed deterministically during the crystal growth. We extract characteristic parameters describing the proximity gap, which is suppressed for lower electron densities and fully developed for larger ones. This gate-tunable transition of the proximity effect can be understood as a transition from the long to the short junction regime of subgap bound states in the NW segment. Our device architecture opens up the way to systematic, quantitative spectroscopy studies of subgap states, such as Majorana-bound states.