The foundation of classical and modern physics rests upon the fundamental paradigm that physical constants remain strictly invariant across space and time. However, developments in modern cosmology, quantum gravity, and higher-dimensional theories suggest that these parameters may not be permanently static, but rather dynamic variables that evolve exceedingly slowly during late stages of the universe. This paper presents a comprehensive theoretical framework conceptualizing physical constants—such as the fine-structure constant, the gravitational constant, and the proton-to-electron mass ratio—as state-dependent variables tied to the overall cosmic evolution. We systematically analyze the theoretical mechanisms governing constant dynamics, including scalar field non-minimal couplings, extra-dimensional compactification dynamics, and phase transitions during cosmic inflation. Furthermore, we explore the dynamic behavior of fundamental interaction strengths across cosmic time and evaluate their profound implications for key unresolved issues, such as cosmic singularity resolution, the nature of dark energy, and the fine-tuning problem. Our findings demonstrate that the observed constancy of fundamental parameters is an asymptotic feature of a low-energy cosmic epoch, and treating constants as dynamic entities opens a promising path toward a unified theory of fundamental interactions.