This paper explores the novel concept of "synthetic dimensions" within the framework of constructive set theory. While synthetic dimensions have gained prominence in physics, particularly in condensed matter systems where additional spatial or internal degrees of freedom are engineered, their rigorous and foundational treatment within constructive mathematics remains largely unexplored. We propose a methodology for defining and constructing such dimensions using intuitionistic logic and the principles of constructive set theory, emphasizing the explicit and verifiable nature of these constructions. The work reviews existing constructive set theories, such as Intuitionistic Zermelo-Fraenkel (IZF) and Constructive Zermelo-Fraenkel (CZF), and investigates how structures analogous to synthetic dimensions, often manifest as indexed families or specific types, can be formally developed without recourse to non-constructive axioms. We present formal definitions and illustrative examples, demonstrating how these synthetically constructed dimensions retain their dimensional properties within a constructive setting. The discussion highlights the philosophical implications of constructive existence for such dimensions and opens new avenues for interdisciplinary research between foundational mathematics and theoretical physics.