DDD-GenDT is a dynamic data-driven generative digital twin framework based on the Dynamic Data-Driven Application Systems (DDDAS) paradigm. To address the high data requirements, data constraints, and inability to adapt to environmental changes of existing digital twins, it consists of a Physical Twin Observation Graph (PTOG), which represents the operating state of a physical twin; Observation Window Extraction, which captures temporal sequences; a Data Preprocessing Pipeline for sensor structuring and filtering; and an LLM ensemble for zero-shot predictive inference. Leveraging generative AI, it enables digital twin construction even in data-poor environments while maintaining industrial data privacy. Through the DDDAS feedback mechanism, it autonomously adapts predictions of physical twin wear and tear to support digital twin aging (DT-aging), ensuring gradual synchronization with the evolution of the physical twin. Validated using the NASA CNC milling dataset, the GPT-4-based digital twin achieved an average RMSE of 0.479 A (4.79% of 10 A spindle current) at zero-shot settings, accurately modeling nonlinear process dynamics and physical twin aging.