We study thermal production of dark matter (DM) in a realization of the minimal models of Bonnefoy et al. [Phys. Rev. Lett. 131, 221802 (2023)PRLTAO0031-900710.1103/PhysRevLett.131.221802], where parity is used to solve the strong CP problem by transforming the entire Standard Model (SM) into a mirror copy. Although the mirror electron e′ is a good DM candidate, its viability is mired by the presence of the mirror up quark u′, whose abundance is intimately related to the e′ abundance and must be suppressed. This can be achieved through a sequential freeze-in mechanism, where mirror photons are first produced from SM gluons, and then the mirror photons produce e′. After computing the details of this double freeze-in, we discuss the allowed parameter space of the model, which lies at the threshold of experimental observations. We find that this origin of e′ DM requires a low reheating temperature after inflation and is consistent with the baryon asymmetry arising from leptogenesis, providing mirror neutrinos have a significant degeneracy. Finally, we show that this e′ DM is not compatible with Higgs parity, the simplest scheme with exact parity, unless SM parameters deviate significantly from their central values or the minimal model is extended.