Ultrathin metal structures have become highly interesting in the field of 2D materials because of their broad range of predicted properties including topological behavior, superconductivity, ferromagnetism, and unique optoelectronic and nonlinear optical properties. However, one of the largest problems presented by the synthesis of 2D metals is the fact that when metals are confined to two dimensions, they become very hard to stabilize and make effectively resistant to oxidation. In this thesis, the process of confinement heteroepitaxy (CHet) is explored as a technique for realizing air-stable, crystalline metals with atomic thicknesses at the epitaxial graphene (EG)/silicon carbide (SiC) interface. Specifically, this work examines the evolution of EG throughout CHet, highlighting the reasons why In intercalation via CHet is successful. The effects of intercalation temperature and variations in the EG are also explored with respect to In intercalation. The development of the CHet process has the potential to broadly impact next generation electronics, photonics, and optoelectronic technologies.