In this work, different types of artificial neural networks are investigated for the estimation of the time of arrival (ToA) in acoustic emission (AE) signals. In particular, convolutional neural network (CNN) models and a novel capsule neural network are proposed in place of standard statistical strategies which cannot handle, with enough robustness, very noisy scenarios and, thus, cannot be sufficiently reliable when the signal statistics are perturbed by local drifts or outliers. This concept was validated with two experiments: the pure ToA identification capability was firstly assessed on synthetic signals for which a ground truth is available, showing a 10× gain in accuracy when compared to the classical Akaike information criterion (AIC). Then, the same models were tested via experimental data acquired in the framework of a localization problem to identify targets with known coordinates on a square aluminum plate, demonstrating an overreaching precision under significant noise levels.