  A large primordial lepton asymmetry is capable of explaining the baryon
asymmetry of the Universe (BAU) through suppression of the electroweak
sphaleron rates (``sphaleron freeze-in") which can lead to a first-order cosmic
QCD transition with an observable gravitational wave (GW) signal. With
next-to-leading order dimensional reduction and the exact 1-loop fluctuation
determinant, we accurately compute the lepton asymmetry needed to realize this
paradigm, finding it to be an order of magnitude smaller than previous
estimates. Further, we apply an improved QCD equation of state capable of
describing the phase transition line together with the critical endpoint
leading to better agreement with lattice and functional QCD results. Based on
this, we identify the range of lepton flavor asymmetries inducing a first-order
cosmic QCD transition. We then extract the parameters relevant to the
prediction of GW signal from a first-order cosmic QCD transition. Our result
showcases the possibility of probing the sphaleron freeze-in paradigm as an
explanation of BAU by future gravitational wave experiments like $\mu$Ares.
