In the context of Smoothed Particle Hydrodynamics (SPH) simulations of solid structures, the initial distribution of particles is of critical importance in ensuring both numerical stability and physical accuracy. Conventional particle distributions, which are typically based on Cartesian lattices due to their inherent regularity, often introduce preferential directions that cause spurious anisotropic stress patterns. This issue is especially evident in plate-like structures that are subjected to dynamic loading, where stress waves may propagate along grid-aligned paths in an artificial manner. This work presents a novel, readily implementable approach for initializing SPH particles in three-dimensional plate geometries. The approach under consideration is inspired by the logic of lamination stacking sequences used in composite materials design. The proposed method generates quasi-isotropic particle distributions by systematically alternating local orientation angles, thereby mimicking the isotropizing effect of laminate lay-ups. This approach has been demonstrated to reduce numerical anisotropy while circumventing the complexity typically associated with advanced pre-processing tools or iterative re-meshing strategies. Indeed, the proposed approach necessitates minimal computational overhead and does not rely on external meshing code, thus facilitating seamless integration into existing commercial SPH workflows. The simulations presented herein were executed using the LS-Dyna software. The validity of the approach is established through a combination of alternative numerical simulations, analytical solutions, and experimental tests involving wave propagation and impact scenarios in plates. The findings indicate a substantial decrease in directionally biased stress and vibration fields in comparison to conventional grid-based particle arrangements while maintaining constant computational cost. The findings obtained from this study align more closely with the experimental and analytical results, thereby enhancing the overall robustness of the SPH simulations for solid mechanics applications involving thin structures, particularly in scenarios where isotropic wave behavior is critical.