Recent work has suggested that black holes (BHs) could be cosmologically coupled to the accelerated expansion of the Universe, potentially becoming a candidate for origin of dark energy. This would imply that BH mass growth follows cosmological expansion, with the masses of individual BHs growing as M_BH ∝ (1 + z)³. In this Letter, we discuss the binary systems Gaia BH1 and Gaia BH2, which contain ∼9 M_⊙ BHs orbited by ∼1 M_⊙ stars in widely separated orbits. The ages of both systems can be constrained by the properties of the luminous stars. If BH masses are indeed growing as (1 + z)³, the masses of both BHs at formation would have been significantly smaller than today. We find a 77% probability that the mass of the BH in Gaia BH2 would have been below 2.2 M_⊙ at formation. This is below the classical Tolman–Oppenheimer–Volkov limit, though it is not yet clear whether or not BHs subject to cosmological coupling should obey this limit. For Gaia BH1, the same probability is 70%. This analysis is consistent with results from two BHs in the globular cluster NGC 3201, but unlike the NGC 3201 BHs, the Gaia BHs have well-constrained inclinations and therefore firm upper mass limits. The discovery of more BHs in binary systems with Gaia astrometry in the coming years will allow us to test the cosmological coupling hypothesis decisively.