Transient sky astronomy is entering a new era with the advent of the Space Variable Objects Monitor mission (SVOM), successfully launched on 22 June 2024. The primary goal of SVOM is to monitor the hard X-ray sky searching for gamma-ray bursts (GRBs). On top of its on-board follow-up capabilities, SVOM will be backed by its ground segment composed of several facilities, including the near-infrared (NIR) imager CAGIRE. Mounted on the robotic telescope COLIBRI, it will be a unique instrument capable of performing fast follow-up of GRB afterglows in the J and H bands, ideal for capturing high-redshift (z$>$6) and/or obscured GRBs. This paper is aimed at estimating the performances of CAGIRE for GRB NIR afterglow detection based on the characteristics of the detector and the specificities of the COLIBRI telescope. Quickly fading GRB afterglows pose challenges that should be addressed by adapting observing strategies to the capabilities of CAGIRE. We used an end-to-end image simulator to produce realistic CAGIRE images, taking into account the results from the characterisation of the ALFA detector used by CAGIRE. We implemented a GRB afterglow generator that simulates infrared light curves and spectra based on published observation of distant GRBs (z$>$6). We retrieved the photometry of nine GRB afterglows in various scenarios covered by CAGIRE. Capturing afterglows as early as one minutes after the burst allows for the identification of a NIR counterpart in the brightest four events. When artificially redshifted even further away, these events remain detectable by CAGIRE up to z=9.6 in the J band and z=13.3 in H band, indicating the pioneering potential of CAGIRE in identifying the most distant GRBs to date.
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