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This work investigates the use of data-driven approaches for reconstructing rough surfaces from scattered sound. The proposed methods stand as alternatives to matrix inversion, which requires a linearisation of the dependence on the surface parameters. Here, a large dataset was formed from different surface realisations alongside the corresponding scattered acoustic field, estimated through the Kirchhoff Approximation. Limiting this work to the reconstruction of a static surface, K-Nearest Neighbours, Random Forests, and a stochastic approach are compared to recover a parameterisation of surfaces using the scattered acoustical pressure as input. The models are then validated against a laboratory experiment alongside methods highlighted in Dolcetti et. al., JSV, 2021. The models are tested at a frequency that best fits the lab uncertainties, then tested on a broad frequency range. This scheme provides relatively accurate results in comparison to the approaches tested. Estimation errors as well as robustness in the presence of noise are discussed.