The pursuit of robust and enhanced acoustic sensing has garnered significant attention across multiple fields of acoustic engineering. Here, we propose a feasible approach to realizing sound energy enhancement along the interface of two topologically distinct materials in an acoustic topological waveguide (ATW) with a gradient gap width. By adjusting the width of the topological bandgap, the sound energy can be localized within a desired region. Benefiting from topological protections, the confinement process is immune to certain types of defects. Our ATW is constructed using two types of C3-symmetric sonic crystals through topology optimization to extremely enlarge the width of the bandgap. Both numerical and experimental results confirm the robust edge states and enhanced energy confinement, even in the presence of non-spin-mixing defects. This work represents an advancement in the design of acoustic functional devices and may inspire potential applications in areas such as acoustic imaging, energy harvesting, and communication systems.