We realize a two-dimensional electron system (2DES) in ZnO by simply depositing pure aluminum on its surface in ultra-high vacuum, and characterize its electronic structure using angle-resolved photoemission spectroscopy. The aluminum oxidizes into alumina by creating oxygen vacancies that dope the bulk conduction band of ZnO and confine the electrons near its surface. The electron density of the 2DES is up to two orders of magnitude higher than those obtained in ZnO heterostructures. The 2DES shows two $s$-type subbands, that we compare to the $d$-like 2DESs in titanates, with clear signatures of many-body interactions that we analyze through a self-consistent extraction of the system self-energy and a modeling as a coupling of a 2D Fermi liquid with a Debye distribution of phonons.