We present coupled ocean-sea-ice simulations of the Middle Jurassic (~165 Ma) when Laurasia and Gondwana began drifting apart and gave rise to the formation of the Atlantic Ocean. Since the opening of the Proto-Caribbean is not well constrained by geological records, configurations with and without an open connection between the Proto-Caribbean and Panthalassa are examined. We use a sea-floor bathymetry obtained by a recently developed three-dimensional (3D) elevation model which compiles geological, palaeogeographical and geophysical data. Our original approach consists in coupling this elevation model, which is based on detailed reconstructions of oceanic realms, with a dynamical ocean circulation model. We find that the Middle Jurassic bathymetry of the Central Atlantic and Proto-Caribbean seaway only allows for a weak current of the order of 2 Sv in the upper 1000 m even if the system is open to the West. The effect of closing the western boundary of the Proto-Caribbean is to increase transport related to barotropic gyres in the southern hemisphere and to change water properties, such as salinity, in the Neo-Tethys. Weak upwelling rates are found in the nascent Atlantic Ocean in the presence of this superficial current and we discuss their compatibility with deep-sea sedimentological records in this region.