Conventional seismic velocity model building in complicated salt-affected areas requires the explicit identification of salt boundaries in migrated images and typically involves testing of possible subsurface scenarios through multiple generations. The resulting velocity models are slow to generate and may contain interpreter-driven features that are difficult to verify. We show that it is possible to build a full final velocity model using advanced forms of full-waveform inversion applied directly to raw field data, starting from a model that contains only a simple 1D compaction trend. This approach rapidly generates the final velocity model and migrates processed reflection data at least as accurately as conventionally generated models. We demonstrate this methodology using an ocean-bottom-node data set acquired in deep water over Walker Ridge in the Gulf of Mexico. Our approach does not require exceptionally long offsets or the deployment of special low-frequency sources. We restrict the inversion so it does not use significant energy below 3 Hz or offsets longer than 14 km. We use three advanced forms of waveform inversion to recover the final model. The first is adaptive waveform inversion to proceed from models that begin far from the true model. The second is nonlinear reflection waveform inversion to recover subsalt velocity structure from reflections and their long-period multiples. The third is constrained waveform inversion to produce salt- and sediment-like velocity floods without explicitly identifying salt boundaries or velocities. In combination, these three algorithms successively improve the velocity model so it fully predicts the raw field data and accurately migrates primary reflections, though explicit migration forms no part of the workflow. Thus, model building via waveform inversion is able to proceed from field data to the final model in just a few weeks. It entirely avoids the many cycles of model rebuilding that may otherwise be required.