Understanding an agent's goal through its behavior is a common AI problem called Goal Recognition (GR). This task becomes particularly challenging in dynamic environments where goals are numerous and ever-changing. We introduce the General Dynamic Goal Recognition (GDGR) problem, a broader definition of GR aimed at real-time adaptation of GR systems. This paper presents two novel approaches to tackle GDGR: (1) GC-AURA, generalizing to new goals using Model-Free Goal-Conditioned Reinforcement Learning, and (2) Meta-AURA, adapting to novel environments with Meta-Reinforcement Learning. We evaluate these methods across diverse environments, demonstrating their ability to achieve rapid adaptation and high GR accuracy under dynamic and noisy conditions. This work is a significant step forward in enabling GR in dynamic and unpredictable real-world environments.