Acoustic metasurfaces are widely used for noise attenuation due to their outstanding acoustic performance and subwavelength characteristics. The paper introduces a topology-optimized inverse design approach for broadband sound-absorbing metasurfaces, aiming to achieve efficient sound absorption performance across a wide frequency spectrum. By integrating genetic algorithms with the finite element method and driven by objectives such as the absorption frequency range and absorption coefficient, we can transcend the limitations of manual design and fully exploit the design potential of structures. Furthermore, the study investigates the sound absorption mechanism and thermal-viscous dissipation through finite element simulations and experimental validations. The research findings reveal that the proposed broadband sound-absorbing metasurfaces demonstrate excellent sound absorption capabilities across the designated frequency range, boasting an average sound absorption coefficient exceeding 85%. These findings offer fresh perspectives and methodologies for advancing the research and practical application of broadband sound-absorbing metasurfaces.