Interfacing a topological insulator (TI) with an s-wave superconductor (SC) is a promising material platform that offers the possibility to realize a topological superconductor through which Majorana-based topologically protected qubits can be engineered. In our computational study of the prototypical SC/TI interface between Nb and Bi₂Te₃, we identify the benefits and possible bottlenecks of this potential Majorana material platform. Bringing Nb in contact with the TI film induces charge doping from the SC to the TI, which shifts the Fermi level into the TI conduction band. For thick TI films, this results in band bending leading to the population of trivial TI quantum-well states at the interface. In the superconducting state, we uncover that the topological surface state experiences a sizable superconducting gap-opening at the SC/TI interface, which is furthermore robust against fluctuations of the Fermi energy. We also show that the trivial interface state is only marginally proximitized, potentially obstructing the realization of Majorana-based qubits in this material platform. This dataset contains the data for the DFT-based calculations for interfaces between the s-wave superconductor Nb and the topological insulator Bi₂Te₃ which is discussed in the publication referenced below.