Acoustic metamaterials (AM) are considered a promising and innovative solution for sound absorption across desired frequency ranges, particularly at low frequencies. They offer potential advancements in meeting application-specific constraints, including spatial arrangements, environmental conditions, and additional functional requirements. Several AM structures have been developed based on the integration of porous materials with hybrid and Helmholtz resonators (i.e., micro-perforated plates, coiled-up/dead-end/extended-tube cavities). In the present work, we reconstruct neural network-based surrogates for estimating the sound absorption performance of acoustic metamaterials made from hybrid resonators. A neural network (NN) architecture is built and trained within the dataset involving input variables (i.e., microstructure and displacement factors) and the sound absorption considered as the output variable. Firstly, the structure–property correlations of acoustic metamaterials are reconstructed using theoretical calculations and numerical simulations. Then, surrogate models for input–output mappings, based on the truncated Karhunen–Loève decomposition combined with neural networks, are reconstructed for characterizing acoustic properties of the AM structure within a limited reference dataset. Finally, the established NN model is examined based on its efficiency and predictive performance with respect to a number of virtual and real material samples. The results obtained from designing acoustic metamaterials are present to demonstrate contributions of the proposed methodology.