A massive, neutral gas reservoir permeating a galaxy proto-cluster after the reionization era

Galaxy clusters are the most massive, gravitationally-bound structures in the Universe, emerging through hierarchical structure formation of large-scale dark matter and baryon overdensities. Early galaxy ``proto-clusters'' are believed to be important physical drivers of the overall cosmic star-formation rate density and serve as ``hotspots'' for the reionization of the intergalactic medium. Our understanding of the formation of these structures at the earliest cosmic epochs is, however, limited to sparse observations of their galaxy members, or based on phenomenological models and cosmological simulations. Here we report the detection of a massive neutral, atomic hydrogen (HI) gas reservoir permeating a galaxy proto-cluster at redshift $z=5.4$, observed one billion years after the Big Bang. The presence of this cold gas is revealed by strong damped Lyman-$\alpha$ absorption features observed in several background galaxy spectra taken with JWST/NIRSpec in close on-sky projection. While overall the sightlines probe a large range in HI column densities, $N_{\rm HI} = 10^{21.7}-10^{23.5}$ cm$^{-2}$, they are similar across nearby sightlines, demonstrating that they probe the same dense, neutral gas. This observation of a massive, large-scale overdensity of cold neutral gas challenges current large-scale cosmological simulations and has strong implications for the reionization topology of the Universe.