Most long gamma-ray bursts (LGRBs) originate from a rare type of massive stellar explosion. Their afterglows, while rapidly fading, can initially be extremely luminous at optical and near-infrared wavelengths, making them detectable at large cosmological distances. Here we report the detection and observations of GRB 250314A by the SVOM satellite and the subsequent follow-up campaign that led to the discovery of the near-infrared afterglow and spectroscopic measurements of its redshift z similar or equal to 7.3. This burst occurred when the Universe was only about 5% of its current age. We discuss the signature of these rare events within the context of the SVOM operating model and the ways to optimise their identification with adapted ground follow-up observation strategies.