Full waveform inversion (FWI) in the North Sea has demonstrated its imaging power starting from low-resolution models obtained by traveltime tomography, enriching them with geologically interpretable fine-scale details. However, building a traveltime-based kinematically accurate starting model for FWI is a time-consuming and rather subjective process requiring phase identification and selection. The two main problems faced by FWI starting from non-informative initial models are the liability to cycle-skipping and a lack of sensitivity to low-wavenumbers in the deep subsurface not sampled by turning waves. On a North Sea ocean-bottom-cable (OBC) 3D dataset, we apply a novel V_p-building methodology that addresses those issues by jointly inverting reflections and refractions (JFWI) using a robust misfit function in the vertical traveltime domain (pseudotime). While pseudotime addresses reflectivity-velocity coupling and attenuates phase-ambiguities at short offsets, a graph-space optimal transport (GSOT) objective function with dedicated data windowing averts cycle-skipping at intermediate-to-long offsets. A fast and balanced reflectivity reconstrution is obtained prior to JFWI thanks to an asymptotic-preconditioned Impedance Waveform Inversion (I_pWI). Starting from a linearly increasing one-dimensional model, GSOT-pseudotime JFWI is effective at obtaining a meaningful P-wave velocity macromodel down to depths sampled by reflections only, without phase identification and picking. P-wave FWI starting from the JFWI-based model, injects the high-wavenumbers missing in the JFWI solution, attaining apparent improvements in both shallow and deep model reconstruction and imaging compared to the previous studies in the literature, and a satisfactory prediction of the ground-truth logs.