  We investigate the possibility that the dark matter abundance is sourced by
the baryon/lepton asymmetry of the early Universe. It turns out that a
Goldstone field of a local classically preserved symmetry in the Standard Model
experiences a kick during a period of baryon/lepton number generation. This
mechanism can be regarded as dynamical generation of initial conditions for
misalignment yet the prediction for relic abundance presents an inverse
dependence on the coupling in parallel with freeze-in vs freeze-out. We explore
two realizations of this mechanism and show that in conjunction with
leptogenesis, it is possible to identify a viable promising region of parameter
space for dark matter production with mass 10 MeV - 1 GeV and decay constant f
in the range of $10^{10} - 10^{12}$ GeV.
