Majorana zero modes, with prospective applications in topological quantum computing, are expected to arise in superconductor/semiconductor interfaces, such as β-Sn and InSb. However, proximity to the superconductor may also adversely affect the semiconductor’s local properties. A tunnel barrier inserted at the interface could resolve this issue. We assess the wide band gap semiconductor, CdTe, as a candidate material to mediate the coupling at the lattice-matched interface between α-Sn and InSb. To this end, we use density functional theory (DFT) with Hubbard U corrections, whose values are machine-learned via Bayesian optimization (BO) [npj Computational Materials 2020, 6, 180]. The results of DFT+U(BO) are validated against angle resolved photoemission spectroscopy (ARPES) experiments for α-Sn and CdTe. For CdTe, the z-unfolding method [Advanced Quantum Technologies 2022, 5, 2100033] is used to resolve the contributions of different k_z values to the ARPES. We then study the band offsets and the penetration depth of metal-induced gap states (MIGS) in bilayer interfaces of InSb/α-Sn, InSb/CdTe, and CdTe/α-Sn, as well as in trilayer interfaces of InSb/CdTe/α-Sn with increasing thickness of CdTe. We find that 16 atomic layers (3.5 nm) of CdTe can serve as a tunnel barrier, effectively shielding the InSb from MIGS from the α-Sn. This may guide the choice of dimensions of the CdTe barrier to mediate the coupling in semiconductor–superconductor devices in future Majorana zero modes experiments.