As biodiversity plummets due to anthropogenic disturbances, the conservation of oceanic species is made harder by limited knowledge of their distributions and migrations. Indeed, tracking species distributions in the open ocean is particularly challenging due to scarce observations, and the complex and variable nature of the ocean system. In this study, we propose a new method that leverages deep learning, specifically convolutional neural networks (CNNs), to capture spatial features of environmental variables. This novelty eliminates the need to predefine these features before modelling and creates opportunities to discover unexpected correlations. Our aim is to present the results of the first trial of this method in the open oceans, discuss limitations, and provide feedback for future improvements or adjustments. In this case study, we considered 38 taxa which include pelagic fishes, elasmobranchs, marine mammals, as well as marine turtles and birds. We trained a model to make probability predictions from the environmental conditions at any specific point in space and time, using species occurrence data from the Global Biodiversity Information Facility (GBIF) and environmental data from various sources. These variables included sea surface temperature, chlorophyll concentration, salinity, and fifteen others. During the testing phase, the model was applied to environmental data at locations where species occurrences were recorded. The model accurately predicted the observed taxon as the most likely taxon in 69% of cases and included the observed taxon among the top three most likely predictions in 89% of cases. These findings show the adequacy of deep learning for species distribution modelling in the open ocean and demonstrate the relevance of CNNs for prospective modelling of the impacts of future ocean conditions on oceanic species. Additionally, this black box model was then analysed with explicability tools to understand which variables had an influence on the model's predictions. While variable importance was species-dependent, we identified finite-size Lyapunov exponents (FSLEs), sea surface temperature, pH, bathymetry and salinity as the most influential variables, in that order. These insights can prove valuable for future species-specific movement ecology studies.