  We reveal that electron-phonon systems described by the Holstein model on a
bipartite lattice exhibit, away from half filling, a supersolid (SS) phase
characterized by coexisting charge order (CO) and superconductivity (SC), and
an accompanying quantum critical point (QCP). The SS, demonstrated by the
dynamical mean-field theory with a quantum Monte Carlo impurity solver, emerges
in the intermediate-coupling regime, where the peak of the Tc dome is located
and the metal-insulator crossover occurs. On the other hand, in the weak- and
strong-coupling regimes the CO-SC boundary is of first order with no
intervening SS phases. The QCP is associated with the continuous transition
from SS to SC and characterized by a reentrant behavior of the SS around it. We
further show that the SS-SC transition is hallmarked by diverging charge
fluctuations and a kink (peak) in the superfluid density.
