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 $z_{T}>5.5times 10^6$ 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.
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