The thermal freeze-out mechanism in its classical form is tightly connected to physics
beyond the Standard Model around the electroweak scale, which has been the target of enormous
experimental efforts. In this work we study a dark matter model in which freeze-out is triggered
by a strong first-order phase transition in a dark sector, and show that this phase transition
must also happen close to the electroweak scale, i.e. in the temperature range relevant for
gravitational wave searches with the LISA mission. Specifically, we consider the spontaneous
breaking of a U(1)′ gauge symmetry through the vacuum expectation value of a scalar field,
which generates the mass of a fermionic dark matter candidate that subsequently annihilates into
dark Higgs and gauge bosons. In this set-up the peak frequency of the gravitational wave
background is tightly correlated with the dark matter relic abundance, and imposing the observed
value for the latter implies that the former must lie in the milli-Hertz range. A peculiar feature
of our set-up is that the dark sector is not necessarily in thermal equilibrium with the Standard
Model during the phase transition, and hence the temperatures of the two sectors evolve
independently. Nevertheless, the requirement that the universe does not enter an extended period
of matter domination after the phase transition, which would strongly dilute any gravitational
wave signal, places a lower bound on the portal coupling that governs the entropy transfer between
the two sectors. As a result, the predictions for the peak frequency of gravitational waves in the
LISA band are robust, while the amplitude can change depending on the initial dark sector
temperature.