Non-invasive subsurface imaging using full waveform inversion (FWI) has the potential to fundamentally change engineering site characterization by enabling the recovery of high resolution 2D/3D maps of subsurface stiffness. Yet, the accuracy of FWI remains quite sensitive to the choice of the initial starting model due to the complexity and non-uniqueness of the inverse problem. In response, we present the novel application of convolutional neural networks (CNNs) to transform an experimental seismic wavefield acquired using a linear array of surface sensors directly into a robust starting model for 2D FWI. We begin by describing three key steps used for developing the CNN, which include: selection of a network architecture, development of a suitable training set, and performance of network training. The ability of the trained CNN to predict a suitable starting model for 2D FWI was compared against other commonly used starting models for a classic near-surface imaging problem; the identification of an undulating, two-layer, soil-bedrock interface. The CNN developed during this study was able to predict complex 2D subsurface images of the testing set directly from their seismic wavefields with an average mean absolute percent error (MAPE) of 6%. When compared to other common approaches, the CNN approach was able to produce starting models with smaller seismic image and waveform misfits, both before and after FWI. The ability of the CNN to generalize to subsurface models which were dissimilar to the ones upon which it was trained was assessed using a more complex, three-layered model. While the predictive ability of the CNN was slightly reduced, it was still able to achieve seismic image and waveform misfits comparable to the other commonly used starting models. This study demonstrates that CNNs have great potential as a tool for developing good starting models for FWI, which are critical for producing accurate FWI results.