ABSTRACT Possible strong first-order hadron-quark phase transitions in neutron star interiors leave an imprint on gravitational waves, which could be detected with planned third-generation interferometers. Given a signal from the late inspiral of a binary neutron star (BNS) coalescence, assessing the presence of such a phase transition depends on the precision that can be attained in the determination of the tidal deformability parameter, as well as on the model used to describe the hybrid star equation of state. For the latter, we employ here a phenomenological meta-modelling of the equation of state that largely spans the parameter space associated with both the low-density phase and the quark high density compatible with current constraints. We show that with a network of third-generation detectors, a single loud BNS event might be sufficient to infer the presence of a phase transition at low baryon densities with an average Bayes factor B ≈ 100, up to a luminosity distance ($\mathcal {D}_\mathrm{ L} \lesssim$ 300 Mpc).