Properties of many layered materials, including copper- and iron-based superconductors, topological insulators, graphite and epitaxial graphene, can be manipulated by the inclusion of different atomic and molecular species between the layers via a process known as intercalation. For example, intercalation in graphite can lead to superconductivity and is crucial in the working cycle of modern batteries and supercapacitors. Intercalation involves complex diffusion processes along and across the layers; however, the microscopic mechanisms and dynamics of these processes are not well understood. Here we report on a novel mechanism for intercalation and entrapment of alkali atoms under epitaxial graphene. We find that the intercalation is adjusted by the van der Waals interaction, with the dynamics governed by defects anchored to graphene wrinkles. Our findings are relevant for the future design and application of graphene-based nano-structures. Similar mechanisms can also have a role for intercalation of layered materials.