Recent theoretical and experimental studies suggest that van der Waals heterostructures with Formula Presented- and Formula Presented-doped bilayers of transition metal dichalcogenides are promising facilitators of exciton superfluidity. Exciton superfluidity in these bilayer systems is often modelled by solving a mean-field gap equation defined for only the conduction and valence band of the electron and hole material, respectively. A key quantity entering the gap equation is the effective Coulomb potential acting as the bare interaction in the subspace of the model. Since the model only includes a few bands around the Fermi energy, the effective model interaction is partially screened. Although the screening is a material-dependent quantity it has, in previous studies, been accounted for in an ad hoc manner, by assuming a static dielectric constant of 2 for a wide range of different materials. In this paper we show that the effective model interaction can be derived from first principles using open source code frameworks. We show that the material dependent screening, accounted for by this ab initio downfolding procedure, has a large influence on the exciton binding energies and superfluid properties. By applying the method to 336 different heterostructures comprised of transition metal dichalcogenides and transition metal oxides we show that the proposed downfolding method yields qualitatively different trends of the exciton binding energies and superfluid properties compared to the standard assumptions with a single dielectric constant. Additionally, we propose material platforms of both transition metal oxides and dichalcogenides with superior properties compared to conventional devices with two transition metal dichalcogenide layers.