Particle physics has long sought to explain the fundamental forces governing the universe, with non-Abelian gauge theories providing a cornerstone for understanding the strong and weak nuclear forces. This study aims to examine the role of these theories in the context of dark matter, a mysterious component of the universe's mass-energy content. Through advanced computational models and recent data from collider experiments, we analyze how non-Abelian gauge symmetries can offer viable candidates for dark matter particles. Our findings suggest that specific gauge groups, particularly SU(3) and SU(2), exhibit properties conducive to stable dark matter candidates. These symmetries provide insights into interaction cross-sections that align with observed cosmic phenomena. In conclusion, the integration of non-Abelian gauge theories into dark matter research not only broadens the scope of particle physics but also enriches our understanding of cosmic evolution. Further experimental validation is recommended to confirm theoretical predictions and enhance the predictive power of these models.