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The race for the most distant object in the Universe has been played by long-duration gamma-ray bursts (GRBs), star-forming galaxies and quasars. GRBs took a temporary lead with the discovery of GRB 090423 at a redshift z=8.2, but now the record-holder is the galaxy GN-z11 at z=11.0. Despite this record, galaxies and quasars are very faint (GN-z11 has a magnitude H=26), hampering the study of the physical properties of the primordial Universe. On the other hand, GRB afterglows are brighter by a factor of >100, with the drawback of lasting only for 1-2 days. Here we describe a novel approach to the discovery of high-redshift (z>6) GRBs, exploiting their near-infrared (nIR) emission properties. Soon after the bright, high-energy prompt phase, a GRB is accompanied by an afterglow. The afterglows of high-redshift GRBs are naturally absorbed, like any other source, at optical wavelengths by Hydrogen along the line of sight in the intergalactic medium (Lyman-alpha absorption). We propose to take advantage of the deep monitoring of the sky by the Vera Rubin Observatory, to simultaneously observe exactly the same fields with a new, dedicated nIR facility. By comparing the two streams of transients, one can pinpoint transients detected in the nIR band and not in the optical band. These fast transients detected only in the nIR and with an AB colour index r-H>3.5 are high-redshift GRBs, with a low contamination rate. Thanks to the depth reached by the Rubin observations, interlopers can be identified, allowing us to discover ~11 GRBs at z>6 per year and ~3 GRBs per year at z>10. This turns out to be one of the most effective probes of the high-redshift Universe.