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This paper discusses the potential of meta-poro-elastic systems with small mass inclusions to create broadband sound absorption performance under the quarter-wavelength limit. A first feasibility study is done to evaluate whether embedding small mass inclusions in specific types of foam can lead to near-perfect absorption at tuned frequencies. This paper includes an optimization routine to find the material properties that maximize the losses due to the mass inclusion such that a near-perfect/perfect absorption coefficient can be achieved at specified frequencies. The near-perfect absorption is due to the mass-spring effect, which leads to an increase in the viscous loss. Therefore, it is efficient in the viscous regime. The well-known critical frequency, which depends on the porosity and flow resistivity of the material, is commonly used as a criteria to distinguish the viscous regime from the inertial regime. However, for the types of foam of interest to this work, the value of critical frequency is below the mass-spring resonance frequency. Hence, the inverse quality factor is used to provides a more accurate estimation on the frequency at which the transition from the viscous regime to the inertial regime.