Hard-magnetic soft materials (HMSMs) are novel class of soft magneto active materials with high remnant characteristics, have shown a great promise owing to their capability to exhibit large reversible deformation under the externally applied magnetic biasing field [1,2]. Because of these characteristics, phononic crystals (PnCs) made up of HMSMs can exhibit band gaps— frequency ranges at which elastic/acoustic waves are forbidden —that are tunable by magnetostatically-controlled deformations [3,4]. Wide band gap PnCs are actually quite desirable for a variety of applications, including elastic/acoustic filters, waveguides, noise suppressors, sensors, acoustic cloaking, and many more. Since band gaps are the primary characteristic of PnCs, topology optimization is one approach to designing microstructures with a desired band gap [5]. In this regard, we propose a gradient-based topology optimization framework to maximize the width of the longitudinal elastic wave band gaps of an infinite periodic hard-magnetic soft material laminate PnCs. In addition to the ideal HMSM model, we use a nonlinear hyperelastic compressible Gent material model to characterise the constitutive behaviour of the phases in the HMSMs phononic structure. To extract the band-structure of the HMSMs phononic structure, an in-house Bloch-Floquet theory-based finite element model is employed. The numerical framework and findings from the present investigation serves as a valuable guidance for designing and manufacturing of futuristic HMSMs wave manipulator with wide tunable band gap characteristics.