Near-Earth asteroid, Kamo'oalewa (469219), is one of a small number of known quasi-satellites of Earth; it transitions between quasi-satellite and horseshoe orbital states on centennial timescales, maintaining this dynamics over megayears. The similarity of its reflectance spectrum to lunar silicates and its Earth-like orbit both suggest that it originated from the lunar surface. Here we carry out numerical simulations of the dynamical evolution of particles launched from different locations on the lunar surface with a range of ejection velocities in order to assess the hypothesis that Kamo`oalewa originated as a debris-fragment from a meteoroidal impact with the lunar surface. As these ejecta escape the Earth-Moon environment, they face a dynamical barrier for entry into Earth's co-orbital space. However, a small fraction of launch conditions yields outcomes that are compatible with Kamo`oalewa's orbit. The most favored conditions are launch velocities slightly above the escape velocity from the trailing lunar hemisphere.