In light of the profound impact of the COVID-19 pandemic on the tourism sector, accurate forecasting of daily visitor arrivals has become paramount. Introduced herein is a novel PROPHET-Bayesian Gaussian Process-Forward Neural Network (PROPHET-BGP-FNN) model, an advanced deep learning (DL) approach, devised for this purpose. This model uniquely integrates the PROPHET model with a deep neural network, merging BGP and FNN, thereby enabling the detection of both linear and nonlinear data attributes. Linear characteristics are discerned by the PROPHET component. Contrary to traditional methodologies which predominantly employ monthly or quarterly datasets, this approach harnesses the precision of daily data, thereby offering a timely and refined forecast. Given the complexity of daily tourist demand data, which manifests a blend of linear and nonlinear patterns, the conventional frameworks often fall short in representation. Through an application on Hawaiian tourism data spanning 2017 to 2021, 80% of which was employed for training and the remainder for validation, it was observed that the PROPHET-BGP-FNN model surpassed benchmark models, including Long Short-Term Memory (LSTM)-SARIMAX-PROPHET, with a remarkable forecast accuracy of 97%. This investigation underscores the viability of integrating high-frequency data with cutting-edge machine learning (ML) methodologies for a more precise forecast in tourism demand. Such insights hold significant implications for strategic decision-making, thereby enhancing the tourism sector's economic viability and competitive stance.