In this paper, we combine a fast wave equation solver using boundary integral methods with a global optimization method, namely Particle Swarm Optimization (PSO), to estimate an initial velocity model. Unlike finite difference methods that discretize the model space into pixels or voxels, our forward solver achieves significant computational savings by constraining the model space to a layered model with perturbations. The speed and reduced model space of the forward solve allows us to use global optimization methods that typically require numerous evaluations and few unknown variables. Our technique does not require an initial guess of a velocity model and is robust to local minima, unlike gradient descent frequently used in methods for both initial velocity model estimation and full waveform inversion. We apply our inversion algorithm to several synthetic data sets and demonstrate how prior information can be used to greatly improve the inversion.