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Using a laser for cutting bones instead of the traditional saws has been shown to improve a patient's healing process. Additionally, the laser has the potential to reduce the collateral damage to the surrounding tissue if appropriately applied. This can be achieved by building additional sensing elements besides the laser itself into an endoscope. To this end, we use a microsecond pulsed Erbium-doped Yttrium Aluminium Garnet (Er:YAG) laser to cut bones. During ablation, each pulse emits an acoustic shock wave that is captured by an air-coupled transducer. In our research, we use the data from these acoustic waves to predict the depth of the cut during the ablation process. We use a Neural Network (NN) to approximate the depth, where we use one or multiple consecutive measurements of acoustic waves. The NN outperforms the base-line method that assumes a constant ablation rate with each pulse to predict the depth. The results are evaluated and compared against the ground-truth depth measurements from Optical Coherence Tomography (OCT) images that measure the depth in realtime during the ablation process.