Many recent studies have pointed out significant discrepancies between observations and models of stellar populations in the near-infrared (NIR). With current and future observing facilities being focused in this wavelength range, properly assessing and solving these issues is of utmost importance. Here, we present the first application of the extragalactic globular cluster (GC) near-infrared spectroscopy survey, and present evidence that these GCs reveal an age zero-point problem of stellar population synthesis (SPS) models. This problem has already been identified in the optical range for the GCs of the Milky Way. Such an issue arises when derived GC spectroscopic ages appear older than the Universe itself. We extend this discussion for the first time to the NIR, specifically using the Paβ line at 1.28 microns. We focus on the GCs of the nearby Centaurus A galaxy using their NIR spectra. This work broadens our understanding of the age zero-point problem and emphasises the necessity to revisit and refine SPS models, especially in the NIR domain.