  The Next-Generation Very Large Array (ngVLA) will revolutionize our
understanding of the Early Universe by tracing the coldest phase of molecular
gas -the raw ingredient for star formation- in the most distant galaxies and
galaxy-clusters. The km-scale core of the ngVLA will be densely packed with
antennas, making it a prime instrument for imaging low-surface-brightness
emission from large-scale molecular gas in the high-z circum- and
inter-galactic medium (CGM/IGM). Recent studies indicate that large amounts of
cold molecular gas are hiding in the 10s-100 kpc environments of distant
galaxies, but that technical limitations on existing telescope arrays have
prevented us from efficiently detecting these large molecular reservoirs. This
may have led to a severely biased view of the molecular Universe. We present
the science case for low-surface-brightness CO observations of the Early
Universe, and how the core of the ngVLA will reveal the cold molecular Universe
to limits and at scales not currently detectable by radio telescopes. As such,
the ngVLA core will be a powerful instrument for studying the cold baryon cycle
that drives the early evolution of galaxies and clusters.
