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In the monolayer limit, 1T' WTe₂ is a two-dimensional (2D) topological insulator exhibiting the quantum spin Hall effect and is believed to host an exciton insulator ground state. However, theoretical analysis is complicated by the difficulty of obtaining consistent descriptions of the single-quasiparticle band structure within conventional first-principles techniques. Previous band structure calculations using the Perdew-Burke-Ernzerhof (PBE) functional and a one-shot GW approximation result in a semimetallic band structure, while calculations with hybrid functionals appear to open a bandgap. Here, we demonstrate that self-consistently updating wavefunctions within a static GW approximation (static COHSEX) can reproduce the band structure experimentally observed by angle-resolved photoemission spectroscopy (ARPES) without resorting to mechanisms beyond the quasiparticle picture. Finally, Bethe–Salpeter equation (BSE) calculation on top of self-consistent GW hint at previously observed negative exciton frequencies, leaving open the possibility of exciton condensation in 1T' monolayer WTe₂.