Biomolecular condensates are cellular phase-separated droplets that usually exhibit a viscoelastic mechanical response, a behavior rationalized by modeling the complex molecules that make up a condensate as stickers and spacers, which assemble into a network-like structure. Condensates usually exhibit a solidification over a long period of time (days), a phenomenon described as aging. The emergence of such a long timescale of evolution from microscopic processes, as well as the associated microscopic reorganization leading to aging, remains mostly an open question. In this article, we explore the connection between the mechanical properties of the condensates and their microscopic structure. We propose a minimal model for the dynamics of stickers and spacers and show that entropy maximization of spacers leads to an attractive force between stickers. Our system displays a surprisingly slow relaxation toward equilibrium, reminiscent of glassy systems and consistent with the liquid-to-solid transition observed. To explain this behavior, we study the clustering dynamics of stickers and successfully explain the origin of glassy relaxation.