  The Hubble tension has now grown to a level of significance which can no
longer be ignored and calls for a solution which, despite a huge number of
attempts, has so far eluded us. Significant efforts in the literature have
focused on early-time modifications of $\Lambda$CDM, introducing new physics
operating prior to recombination and reducing the sound horizon. In this
opinion paper I argue that early-time new physics alone will always fall short
of fully solving the Hubble tension. I base my arguments on seven independent
hints, related to 1) the ages of the oldest astrophysical objects, 2)
considerations on the sound horizon-Hubble constant degeneracy directions in
cosmological data, 3) the important role of cosmic chronometers, 4) a number of
``descending trends'' observed in a wide variety of low-redshift datasets, 5)
the early integrated Sachs-Wolfe effect as an early-time consistency test of
$\Lambda$CDM, 6) early-Universe physics insensitive and uncalibrated cosmic
standard constraints on the matter density, and finally 7) equality
wavenumber-based constraints on the Hubble constant from galaxy power spectrum
measurements. I argue that a promising way forward should ultimately involve a
combination of early- and late-time (but non-local -- in a cosmological sense,
i.e. at high redshift) new physics, as well as local (i.e. at $z \sim 0$) new
physics, and I conclude by providing reflections with regards to potentially
interesting models which may also help with the $S_8$ tension.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory