We explore the Higgs particle in the cosmic quark-gluon plasma (QGP) below the electroweak phase transition temperature $T_\mathrm{EW}\simeq 125\mathrm{\,GeV}$. We show that Higgs is neither in abundance (chemical) nor in momentum distribution equilibrium in certain stages of the Universe evolution. Nonequilibrium originates in: For chemical nonequilibrium in the always present irreversible decays into virtual heavy gauge bosons, and; For $T<25$\,GeV in relatively rapid $2\leftrightarrow 1$ formation and decay processes yielding momentum distribution as created in these reactions. As heavy particles disappear, the minimal Higgs coupling to abundant low mass particles fails in $2\to2$ (two-particle) scattering processes to assure a kinetic distribution equilibrium. The expansion of the Universe is by more than 10 orders of magnitude slower compared to microscopic processes. All other particles in the Universe are in full thermal equilibrium, with exception of the late in QGP evolution of the bottom flavor near to hadronization condition.