  Kinetic equilibration of the matter and baryon densities attained in central
region of colliding Au+Au nuclei in the energy range of $\sqrt{s_{NN}}=$
3.3--39 GeV are examined within the model of the three-fluid dynamics. It is
found that the kinetic equilibration is faster at higher collision energies:
the equilibration time (in the c.m. frame of colliding nuclei) rises from
$\sim$5 fm/c at $\sqrt{s_{NN}}=$ 3.3 GeV to $\sim$1 fm/c at 39 GeV. The
chemical equilibration, and thus thermalization, takes longer. We argue that
the presented time evolution of the net-baryon and energy densities in the
central region is a necessary prerequisite of proper reproduction of bulk
observables in midrapidity. We suggest that for informative comparison of
predictions of different models it is useful to calculate an invariant 4-volume
($V_4$), where the proper density the equilibrated matter exceeds certain
value. The advantage of this 4-volume is that it does not depend on specific
choice of the 3-volume in different studies and takes into account the lifetime
of the high-density region, which also matters. The 4-volume $V_4=$ 100
fm$^4$/c is chosen to compare the baryon densities attainable at different
different energies. It is found that the highest proper baryon density
increases with the collision energy rise, from $n_B/n_0\approx$ 4 at 3.3 GeV to
$n_B/n_0\approx$ 30 at 39 GeV. These highest densities are achieved in the
central region of colliding system.
