The Universe may feature large-scale inhomogeneities beyond the standard paradigm, implying that statistical homogeneity and isotropy may be reached only on much larger scales than the usually assumed ∼100 Mpc. This means that we are not necessarily typical observers and that the Copernican principle could be recovered only on super-Hubble scales. Here, we do not assume the validity of the Copernican principle and let Cosmic Microwave Background, Baryon Acoustic Oscillations, type Ia supernovae, local H0, cosmic chronometers, Compton y-distortion and kinetic Sunyaev-Zeldovich observations constrain the geometrical degrees of freedom of the local structure, which we parametrize via the ΛLTB model — basically a non-linear radial perturbation of a FLRW metric. In order to quantify if a non-Copernican structure could explain away the Hubble tension, we pay careful attention to computing the Hubble constant in an inhomogeneous universe, and we adopt model selection via both the Bayes factor and the Akaike information criterion. Our results show that, while the ΛLTB model can successfully explain away the H0 tension, it is favored with respect to the ΛCDM model only if one solely considers supernovae in the redshift range that is used to fit the Hubble constant, that is, 0.023<z<0.15. If one considers all the supernova sample, then the H0 tension is not solved and the support for the ΛLTB model vanishes. Combined with other data sets, this solution to the Hubble tension barely helps. Finally, we have reconstructed our local spacetime. We have found that data are best fit by a shallow void with δL≈−0.04 and routL≈300 Mpc, which, interestingly, lies on the border of the 95\% credible region relative to the standard model expectation.