The near-Earth asteroid (469219) Kamo`oalewa is one of a handful of known quasi-satellites of Earth. Numerical solutions show that on timescales of decades or centuries, it transitions between quasi-satellite and horseshoe orbital states, maintaining this behavior for the order of megayears. Little is known about its physical properties and origins. Considering its Earth-like orbit, we explore the hypothesis that it might have originated in the Earth-Moon system as a fragment of the Moon, as debris from a meteoroidal impact with the Moon’s surface. We carry out numerical simulations of test particles ejected from the Moon surface at different locations and with a range of ejection velocities. The set of initial conditions has been constrained to look for trajectories compatible with Kamo`oalewa’s dynamical behavior, exploring the possible lunar origin of this asteroid. These simulations are performed using the REBOUND software package. Besides potentially identifying a plausible origin for Kamo`oalewa or other dynamically similar near-Earth objects, these simulations also enable exploration of the rich dynamics of particles around the Earth-Moon system.