An acoustic topological insulator (TI) is synthesized using topology optimization, a free material inverse design method. The TI appears spontaneously from the optimization process without imposing explicit requirements on the existence of pseudospin-1/2 states at the TI interface edge, or the Chern number of the topological phases. The resulting TI is passive, consisting of acoustically hard members placed in an air background and has an operational bandwidth of ≈12.5% showing high transmission. Further analysis demonstrates confinement of more than 99% of the total field intensity in the TI within at most six lattice constants from the TI interface. The proposed design hereby outperforms a reference from recent literature regarding energy transmission, field confinement, and operational bandwidth.