Long-duration gamma-ray burst (GRB) afterglow observations offer cutting-edge opportunities to characterise the star formation history of the Universe back to the epoch of reionisation, and to measure the chemical composition of interstellar and intergalactic gas through absorption spectroscopy. The main barrier to progress is the low efficiency in rapidly and confidently identifying which bursts are high redshift ( $z > 5$ ) candidates before they fade, as this requires low-latency follow-up observations at near-infrared wavelengths (or longer) to determine a reliable photometric redshift estimate. Since no current or planned gamma-ray observatories carry near-infrared telescopes on-board, complementary facilities are needed. So far this task has been performed by instruments on the ground, but sky visibility and weather constraints limit the number of GRB targets that can be observed and the speed at which follow-up is possible. In this work we develop a Monte Carlo simulation framework to investigate an alternative approach based on the use of a rapid-response near-infrared nano-satellite, capable of simultaneous imaging in four bands from $0.8$ to $1.7\,\unicode{x03BC}$ m (a mission concept called SkyHopper). Using as reference a sample of 88 afterglows observed with the GROND instrument on the MPG/ESO telescope, we find that such a nano-satellite is capable of detecting in the H-band (1.6 $\unicode{x03BC}$ m) $72.5\% \pm 3.1\%$ of GRBs concurrently observable with the Swift satellite via its UVOT instrument (and $44.1\% \pm 12.3\%$ of high redshift ( $z>5$ ) GRBs) within 60 min of the GRB prompt emission. This corresponds to detecting ${\sim}55$ GRB afterglows per year, of which 1–3 have $z > 5$ . These rates represent a substantial contribution to the field of high-z GRB science, as only 23 $z > 5$ GRBs have been collectively discovered by the entire astronomical community over the last ${\sim}24$ yr. Future discoveries are critically needed to take advantage of next generation follow-up spectroscopic facilities such as 30m-class ground telescopes and the James Webb Space Telescope. Furthermore, a systematic space-based follow-up of afterglows in the near-infrared will offer new insight on the population of dusty (‘dark’) GRBs which are primarily found at cosmic noon ( $z\sim 1-3$ ). Additionally, we find that launching a mini-constellation of 3 near-infrared nano-satellites would increase the detection fraction of afterglows to ${\sim}83\%$ and substantially reduce the latency in the photometric redshift determination.