ABSTRACT As the primary fuel for star formation, molecular gas plays a key role in galaxy evolution. A number of techniques have been used for deriving the mass of molecular reservoirs in the early Universe (e.g. [C ii]158 µm, [C i], dust continuum), but the standard approach of CO-based estimates has been limited to a small number of galaxies due to the intrinsic faintness of the line. We present Jansky Very Large Array observations of the $z∼ \, 8.31$ galaxy MACS0416_Y1, targeting CO(2-1) and rest-frame radio continuum emission, which result in upper limits on both quantities. Adding our continuum limit to the published far-infrared (FIR) spectral energy distribution, we find a small non-thermal contribution to the FIR emission, a low-dust mass (${\rm {\log }}_{10}({\rm {\mathit{ M}}}_{\rm {D}}/{\rm M}_{⊙ })∼ 5$), and an abnormally high-dust temperature (${\rm \mathit{ T}}_{\rm D}\gtrsim \, 90\, \mathrm{ K}$) that may indicate a recent starburst. Assuming a low metallicity (Z/Z⊙ ∼ 0.25), we find evidence for $M_{{\rm {H}}_2}, \mathrm{ CO}\lesssim \, 10^{10}$ M⊙, in agreement with previous [C ii] investigations ($M_{{\rm {H}}_2},[\mathrm{ C}\,\small{\rm II}]\, ∼ \, 10^{9.6}$ M⊙). Upcoming JWST observations of this source will result in a precise determination of Z, enabling better constraints and an unprecedented view of the gaseous reservoir in this primordial starburst galaxy.