Following the discovery of the quantum Hall effect and topological insulators the topological properties of classical waves began to draw attention. Topologically non-trivial bands characterized by non-zero Chern numbers are realized through either the breaking of time-reversal symmetry using an external magnetic field or dynamic modulation. Owing to the absence of a Faraday-like effect, the breaking of time-reversal symmetry in an acoustic system is commonly realized with moving background fluids, which drastically increases the engineering complexity. Here we show that we can realize effective inversion symmetry breaking and create an effective gauge flux in a reduced two-dimensional system by engineering interlayer couplings, achieving an acoustic analogue of the topological Haldane model. We show that the synthetic gauge flux is closely related to Weyl points in the three-dimensional band structure and the system supports chiral edge states for fixed values of kz.