A key to understanding the formation of the first galaxies is to quantify the content of the molecular gas as the fuel for star formation activity through the epoch of reionization. In this paper, we use the 158µm [C II] fine-structure emission line as a tracer of the molecular gas in the interstellar medium (ISM) in a sample of 𝓏 = 6.5–7.5 galaxies recently unveiled by the Reionization Era Bright Line Emission Survey, REBELS, with the Atacama Large Millimeter/submillimeter Array. We find substantial amounts of molecular gas (~1010.5 M⊙), comparable to those found in lower-redshift galaxies for similar stellar masses (~1010 M⊙). The REBELS galaxies appear to follow the standard scaling relations of the molecular gas-to-stellar mass ratio (µmol) and the gas-depletion timescale (tdep) with distance to the star-forming main sequence expected from extrapolations of 𝓏 ~ 1–4 observations. We find median values at 𝓏 ~ 7 of μmol = 2.6−1.44.1 and tdep = 0.5−0.14+0.26 Gyr, indicating that the baryonic content of these galaxies is dominated by the gas phase and evolves little from 𝓏 ~ 7 to 4. Our measurements of the cosmic density of molecular gas, log(ρmol/(M⊙ Mpc−3)) = 6.34−0.31+0.34, indicate a steady increase by an order of magnitude from 𝓏 ~ 7 to 4.