Using X-ray photoemission spectroscopy (XPS) and scanning tunneling microscopy (STM) we resolve the temperature-, time-, and flake size-dependent intercalation phases of oxygen underneath graphene on Ir(111) formed upon exposure to molecular oxygen. Through the applied pressure of molecular oxygen the atomic oxygen created on the bare Ir terraces is driven underneath graphene flakes. The importance of substrate steps and of the unbinding of graphene flake edges from the substrate for the intercalation is identified. With the use of CO titration to selectively remove oxygen from the bare Ir terraces the energetics of intercalation is uncovered. Cluster decoration techniques are used as an efficient tool to visualize intercalation processes in real space.