Quantum chromodynamics (QCD), the basic theory of strong interactions between the quarks and gluons is expected to play an important role in the early universe. We discuss the scenario when the fast cooling of QCD matter leads to the creation of a saturated phase with an enormous number of possible configurations. Using an analogy with the classical glasses we predict that this glassy form of matter -- the Glasma -- existing at temperatures above a few GeV has dominated properties of the universe in the period preceding the formation of quark-gluon plasma (QGP). We examine the possibility that the properties of this high-temperature color-glass condensate (CGC) filling the universe in the very hot QCD and EW eras, and beyond were close to the stiff matter.