  Currently, the standard cosmological model faces some tensions and
discrepancies between observations at early and late cosmological time. One of
them concerns the well-known $H_0$-tension problem, i.e., a
$\sim4.4\sigma$-difference between the early-time estimate and late-time
measurements of the Hubble constant, $H_0$. Another puzzling question rests in
the cosmological lithium abundance, where again local measurements differ from
the one predicted by Big Bang Nucleosynthesis (BBN). In this work, we show that
a mechanism of light dark matter production might hold the answer for these
questions. If dark matter particles are sufficiently light and a fraction of
them was produced non-thermally in association with photons, this mechanism has
precisely what is needed to destroy Lithium without spoiling other BBN
predictions. Besides, it produces enough radiation that leads to a larger $H_0$
value, reconciling early and late-time measurements of the Hubble expansion
rate without leaving sizable spectral distortions in the Cosmic Microwave
Background spectrum.
