The next generation of wireless networks will utilize highly directional beams to overcome the path loss at high frequencies, requiring angle inference during link establishment. Furthermore, the integration of location-based services into the wireless infrastructure is rapidly increasing, bringing in a significant demand for an integrated fast localization scheme. In this work, we present a first-of-its-kind one-shot angular localization method that is carried out with a re-configurable architecture that unlocks ISAC functionality. Specifically, we use an electrically tunable metasurface with broadband response to generate wavefronts that are randomized across the angular space with diverse wideband amplitude and phase observations, corresponding to a collection of angle-unique one-shot beacons. Our results show down to 0.26° mean absolute error at 20 dB SNR, an order of magnitude improvement over the recently proposed one-shot solutions based on leaky-wave antennas (LWAs), in addition to having wider area coverage and less stringent bandwidth requirements.