  We investigate a mechanism for the production of self-interacting dark matter
based on WIMP-like messenger state decays into dark matter and dark radiation
occurring after recombination. Such a transition leads to a mild relaxation of
the Hubble tension, and at the same time may resolve the small-scale structure
problems of the $\Lambda$CDM. We illustrate this mechanism in the Higgs portal
dark matter model, which we find to be a promising route.
