  We study the spectral properties of SU(3) gauge theory with and without
dynamical quarks (QCD) at thermal equilibrium using lattice gauge theory
techniques. By measuring eigenstates of a massless overlap Dirac operator on
the gauge configurations, we provide a gauge invariant method to study spectral
properties of non-Abelian gauge theories. Whereas the majority of these
eigenstates below the magnetic scale have universal nearest-neighbor level
spacing fluctuations consistent with certain class of random matrix theories at
temperatures away from the chiral crossover transition in QCD, a few among them
start to become prominent just above the crossover forming clusters percolating
over the entire volume. By matching the non-perturbative magnetic scales in a
high temperature thermal state and a particular non-equilibrium chaotic state
of QCD, we provide an estimate of thermalization time $\sim 1.44$ fm/c.
