Waste management represents a critical issue that industrialized countries must necessarily deal with. Sustainable architecture involves the reuse of materials with the aim of significantly reducing the amount of waste produced. In this study, a new layered membrane metamaterial was developed based on three layers of a reused PVC membrane and reused metal washers attached. The membranes were fixed to a rigid support, leaving a cavity between the stacked layers. The samples were used to measure the sound absorption coefficient with an impedance tube. Different configurations were analyzed, changing the number of masses attached to each layer and the geometry of their position. These measurements were subsequently used to train a model based on artificial neural networks for the prediction of the sound absorption coefficient. This model was then used to identify the metamaterial configuration that returns the best absorption performance. The designed metamaterial behaves like an acoustic absorber even at low frequencies.