The axion is a hypothetical boson arising from the most natural solution to the problem of charge and parity symmetry in the strong nuclear force. Moreover, this pseudoscalar emerges as a dark matter candidate in a parameter space extending several decades in mass. The Dark-photons & Axion-Like particles Interferometer (DALI) is a proposal to search for axion dark matter in a range that remains under-examined. Currently in a design and prototyping phase, this haloscope is a multilayer Fabry-Pérot interferometer. A proof-of-principle experiment is performed to observe the resonance in a prototype. The test unveils a quality factor per layer of a few hundred over a bandwidth of the order of dozens of megahertz. The result elucidates a physics potential to find the, so far elusive, axion, in a sector which can simultaneously solve the symmetry problem in the strong interaction and the enigma of dark matter.