Time delay estimation between signals propagating through nonlinear media is an important problem with application to radar, underwater acoustics, damage detection, and communications (to name a few). Here, we describe a simple approach for determining the time delay between two such signals via minimization of the one-dimensional Wasserstein distance. The solution can be computed efficiently digitally in O(N), or in linear time in circuitry. We demonstrate the approach in the estimation of time delay between acoustic (Lamb) waves generated in an aluminum plate, and compare to alternative approaches.