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During catastrophic events like natural disasters, pandemics, large-scale industrial accidents, or wars, hospitals must continue providing uninterrupted healthcare services despite significant challenges. However, they might also become victims of the disaster and face the necessity of evacuation. Existing hospital evacuation models, which primarily depend on essential data being available before evacuation, often fail to account for the dynamic nature of emergencies and oversimplify the complexities of real-world situations. This paper marks a paradigm shift towards a real-time, data-driven decision-support model for managing hospital evacuations during acute emergencies. The proposed model integrates data on factors such as the severity of the situation, resource status, patient needs, and road conditions. It employs a Bayesian ARIMA component to predict patient arrivals, specially tailored for limited sample sizes. A case study of a hypothetical flood emergency in the Hawkesbury-Nepean Rivers region in Western Sydney, Australia, demonstrates the advantages of a proposed framework equipped with predictive analytics compared to a purely optimization-based model. Numerical testing reveals that without a forward-looking component to predict patient transfer demand over future periods, there can be a misallocation of resources in the initial stages, leading to shortages of critical resources later in the emergency operation. The proposed dynamic decision support framework underlines the potential value of predictive analytics for anticipating future trends in disaster management and response. The findings offer potential advancements in understanding how data and technology can be harnessed to improve emergency responses, promoting more resilient healthcare systems.