Non-Hermitian physics, characterized by energy dissipation and amplification, has attracted significant attention in recent years. These systems exhibit unique physical phenomena that are absent in Hermitian systems [1]. While originally developed in quantum contexts, this theoretical framework is increasingly being applied to classical engineering fields, including acoustic metamaterials and viscoelastic media. Motivated by these developments, this study focuses on design methods for non-Hermitian devices using viscoelastic composites. It is known that theoretical bounds exist for the effective complex bulk and shear moduli of two-phase isotropic viscoelastic composites, determined by the properties of the constituent materials [2]. However, it has not been sufficiently verified whether microstructures corresponding to the interior of these theoretical bounds exist. In this study, we numerically verify this feasibility based on a complex-valued homogenization method using a 6mm hexagonal lattice unit cell, which guarantees macroscopic isotropy. First, we investigate the range of achievable complex moduli through an empirical approach by varying basic shape parameters such as laminate and circular geometries. Furthermore, to realize specific regions within the bounds that are difficult to reach with empirical methods, we apply a topology optimization method to minimize the error from a target complex modulus. The method established in this study reveals the range of achievable complex moduli in isotropic two-phase viscoelastic composites. The results of this study aim to contribute to the design of composite materials for realizing non-Hermitian physical phenomena.