  A small fraction of thermalized dark radiation that transitions into cold
dark matter (CDM) between big bang nucleosynthesis and matter-radiation
equality can account for the entire dark matter relic density. Because of its
transition from dark radiation, "late-forming dark matter" (LFDM) suppresses
the growth of linear matter perturbations and imprints the oscillatory
signatures of dark radiation perturbations on small scales. The cutoff scale in
the linear matter power spectrum is set by the redshift $z_T$ of the phase
transition; tracers of small-scale structure can therefore be used to infer the
LFDM formation epoch. Here, we use a forward model of the Milky Way (MW)
satellite galaxy population to address the question: How late can dark matter
form? For dark radiation with strong self-interactions, which arises in
theories of neutrinolike LFDM, we report $z_{T}>5.5\times 10^6$ at $95\%$
confidence based on the abundance of known MW satellite galaxies. This limit
rigorously accounts for observational incompleteness corrections, marginalizes
over uncertainties in the connection between dwarf galaxies and dark matter
halos, and improves upon galaxy clustering and Lyman-$\alpha$ forest
constraints by nearly an order of magnitude. We show that this limit can also
be interpreted as a lower bound on $z_T$ for LFDM that free-streams prior to
its phase transition, although dedicated simulations will be needed to analyze
this case in detail. Thus, dark matter created by a transition from dark
radiation must form no later than one week after the big bang.
