Developing fast and accurate surrogates for physics-based coastal and ocean models is an urgent need due to the coastal flood risk under accelerating sea level rise, and the computational expense of deterministic numerical models. For this purpose, we develop the first digital twin of Earth coastlines with new physics-informed machine learning techniques extending the state-of-art Neural Operator. As a proof-of-concept study, we built Fourier Neural Operator (FNO) surrogates on the simulations of an industry-standard flood and ocean model (NEMO). The resulting FNO surrogate accurately predicts the sea surface height in most regions while achieving upwards of 45x acceleration of NEMO. We delivered an open-source CoastalTwin platform in an end-to-end and modular way, to enable easy extensions to other simulations and ML-based surrogate methods. Our results and deliverable provide a promising approach to massively accelerate coastal dynamics simulators, which can enable scientists to efficiently execute many simulations for decision-making, uncertainty quantification, and other research activities.