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We present the validation of a transiting low-density exoplanet orbiting the M2.5 dwarf TOI 620 discovered by the NASA TESS mission. We utilize photometric data from both TESS and ground-based follow-up observations to validate the ephemerides of the 5.09-day transiting signal and vet false positive scenarios. High-contrast imaging data are used to resolve the stellar host and exclude stellar companions at separations $\gtrsim 0.2''$. We obtain follow-up spectroscopy and corresponding precise radial velocities (RVs) with multiple PRV spectrographs to confirm the planetary nature of the transiting exoplanet. We calculate a 5$σ$ upper limit of $M_P < 7.1$ M$_\oplus$ and $ρ_P < 0.74$ g cm$^{-3}$, and we identify a non-transiting 17.7-day candidate. We also find evidence for a substellar (1-20 M$_{\rm J}$) companion with a projected separation $\lesssim 20$ au from a combined analysis of Gaia, AO imaging, and RVs. With the discovery of this outer companion, we carry out a detailed exploration of the possibilities that TOI 620 b might instead be a circum-secondary planet or a pair of eclipsing binary stars orbiting the host in a hierarchical triple system. We find, under scrutiny, that we can exclude both of these scenarios from the multi-wavelength transit photometry, thus validating TOI 620 b as a low-density exoplanet transiting the central star in this system. The low density of TOI 620 b makes it one of the most amenable exoplanets for atmospheric characterization, such as with JWST and Ariel, validated or confirmed by the TESS mission to date.