Detailed reconstruction of deep structures with full-waveform inversion (FWI) of wide-angle ocean-bottom seismometer (OBS) data remains challenging and unconventional. The complexity of the long-offset waveforms increases the nonlinearity of the inverse problem, while the sparsity of the OBS deployments leads to a poorly constrained model reconstruction. Consequently, for such a FWI setting it is difficult to derive an initial model that satisfies the cycle-skipping criterion. Searching for a remedy to this issue, we investigate the graph-space optimal transport (GSOT) technique, which can potentially overcome the cycle-skipping problem at the initial FWI stage. The key feature of the GSOT cost function is the convexity with respect to the patterns in the two seismograms, which allows for correct matching of the arrivals shifted in time for more than half of the wavelet. This in turn shall allow FWI to handle the large kinematic errors of the starting model. We test this hypothesis by applying the time-domain acoustic FWI to the synthetic and field data from the subduction zone environment. We show that despite the complexity of the geological structure, the GSOT misfit function is able to guide the FWI toward the precise velocity model reconstruction and data fitting starting from a simple 1D model. The improved convexity of the GSOT misfit function allows FWI to converge even when mismatches between the observed and synthetic signals reach a few cycles. This ability reduces the constraint on the kinematic accuracy of the initial model and makes the FWI from the OBS data more feasible.