Statistical properties of multidimensional Burgers' turbulence evolving in the presence of a force field with random potential, which is delta-correlated in time and smooth in space, are studied in the inviscid limit and at the physical level of rigorousness. The solution algorithm reduces to finding multistream fields describing the motion of an auxiliary gas of interacting particles in a force field. Consequently, the statistical description of forced Burgers' turbulence is obtained by finding the largest possible value of the least action for the auxiliary gas. The exponential growth of the number of streams is found to be a necessary condition for the existence of stationary regimes.