If strange quark matter (SQM) is absolutely stable, hadronic neutron stars (NSs) and strange quark stars (QSs) may coexist in the so-called two-families scenario. A key issue is explaining how hadronic NSs can survive as long-lived metastable objects, rather than promptly converting into stable QSs. Since all NSs are born as hot proto-neutron stars (PNSs), a necessary condition for their existence is that the conditions for conversion, triggered by the nucleation of the first critical SQM droplet, are not reached in every PNS. We investigate the thermal nucleation of critical SQM droplets under representative PNS conditions, accounting for flavor-composition fluctuations and finite-size effects on color superconductivity by suppressing pairing in droplets smaller than the diquark coherence length. We define the nucleation conditions as the thermodynamic state at which a critical SQM droplet is expected to nucleate statistically within the characteristic dynamical timescale of the system. Under these conditions, the reduced nucleation barrier is nearly universal, with $\Ws/T\simeq167$ to within a few units. Exploring the SQM parameter space of a bag-like model, with a fixed hadronic EOS compatible with a recent Bayesian analysis of the two-families scenario, we find parametrizations and surface tensions for which a canonical $1.4\Msol$ NS survives the PNS stage, a necessary condition for the two-families scenario. For this specific combination of hadronic and quark models, requiring such survival sets a lower bound on the hadron–quark surface tension, $\sigma\gtrsim 67\MeVfm$.