  The recent analysis from the SH0ES Collaboration has confirmed the existence
of a Hubble tension between measurements at high redshift ($z> 1000$) and at
low redshift ($z<1$) at the $5\sigma$ level with the low redshift measurement
giving a higher value. In this work we propose a particle physics model that
can help alleviate the Hubble tension via an out-of-equilibrium hidden sector
coupled to the visible sector. The particles that populate the dark sector
consist of a dark fermion, which acts as dark matter, a dark photon, a massive
scalar and a massless pseudo-scalar. Assuming no initial population of
particles in the dark sector, feeble couplings between the visible and the
hidden sectors via kinetic mixing populate the dark sector even though the
number densities of hidden sector particles never reach their equilibrium
distribution and the two sectors remain at different temperatures. A
cosmologically consistent analysis is presented where a correlated evolution of
the visible and the hidden sectors with coupled Boltzmann equations involving
two temperatures, one for the visible sector and the other for the hidden
sector, is carried out. The relic density of the dark matter constituted of
dark fermions is computed in this two-temperature formalism. As a consequence,
BBN predictions are upheld with a minimal contribution to $\Delta N_{\rm eff}$.
However, the out-of-equilibrium decay of the massive scalar to the massless
pseudo-scalar close to the recombination time causes an increase in $\Delta
N_{\rm eff}$ that can help weaken the Hubble tension.
