  Our knowledge of galaxy formation and evolution has incredibly progressed
through multi-wavelength observational constraints of the interstellar medium
(ISM) of galaxies at all cosmic epochs. However, little is known about the
physical properties of the more diffuse and lower surface brightness reservoir
of gas and dust that extends beyond ISM scales and fills dark matter haloes of
galaxies up to their virial radii, the circumgalactic medium (CGM). New
theoretical studies increasingly stress the relevance of the latter for
understanding the feedback and feeding mechanisms that shape galaxies across
cosmic times, whose cumulative effects leave clear imprints into the CGM.
Recent studies are showing that a -- so far unconstrained -- fraction of the
CGM mass may reside in the cold (T < 1e4 K) molecular and atomic phase,
especially in high-redshift dense environments. These gas phases, together with
the warmer ionised phase, can be studied in galaxies from z ~ 0 to z ~ 10
through bright far-infrared and sub-millimeter emission lines such as [C II]
158${\mu}$m, [O III] 88 ${\mu}$m, [C I] 609${\mu}$m, [C I] 370${\mu}$m, and the
rotational transitions of CO. Imaging such hidden cold CGM can lead to a
breakthrough in galaxy evolution studies but requires a new facility with the
specifications of the proposed Atacama Large Aperture Submillimeter Telescope
(AtLAST). In this paper, we use theoretical and empirical arguments to motivate
future ambitious CGM observations with AtLAST and describe the technical
requirements needed for the telescope and its instrumentation to perform such
science.
