We investigated ion acceleration by an electrostatic shock in an exploded target irradiated by an ultrashort, circularly polarized laser pulse by means of one- and three-dimensional particle-in-cell simulations. We discovered that the laser field penetrating via relativistic transparency (RT) rapidly heated the upstream electron plasma to enable the formation of a high-speed electrostatic shock. Owing to the RT-based rapid heating and the fast compression of the initial density spike by a circularly polarized pulse, a new regime of the shock ion acceleration driven by an ultrashort (20-40 fs), moderately intense (1-1.4 PW) laser pulse is envisaged. This regime enables more efficient shock ion acceleration under a limited total pulse energy than a linearly polarized pulse with crystal laser systems of lambda similar to 1 mu m