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FeTe_0.55Se_0.45 (FTS) occupies a special spot in modern condensed matter physics at the intersections of electron correlation, topology, and unconventional superconductivity. The bulk electronic structure of FTS is predicted to be topologically nontrivial thanks to the band inversion between the d_xz and p_z bands along Γ-Z. This in turn would give rise to a Dirac surface state (DSS) hosting topological superconductivity below the bulk superconducting temperature. However, whether this prediction is indeed realized in FTS remains controversial in recent angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling spectroscopy (STS) studies. In ARPES experiments, a Dirac-cone-like feature has been identified, yet only at certain out-of-plane momenta (k_z), leading to speculations that it might originate from a bulk band instead of the DSS. Moreover, the measured band structure differs significantly from the density functional theory (DFT) predictions, with no direct observations of either the p_z band or the bulk band inversion. Here we resolve this debate through a comprehensive ARPES investigation. We first observe a persistent DSS independent of k_z. Then, by comparing FTS with FeSe which has no band inversion along Γ-Z, we identify the spectral weight fingerprint of both the presence of the p_z band and inversion between the d_xz and p_z bands. Our results highlight the impact of strong correlation and large spin-orbit coupling in FTS and make a strong case for the existence of topological band structure in this unconventional superconductor.