  Whilst young massive clusters (YMCs; $M$ $\gtrsim$ 10$^{4}$ M$_{\odot}$, age
$\lesssim$ 100 Myr) have been identified in significant numbers, their
progenitor gas clouds have eluded detection. Recently, four extreme molecular
clouds residing within 200 pc of the Galactic centre have been identified as
having the properties thought necessary to form YMCs. Here we utilise far-IR
continuum data from the Herschel Infrared Galactic Plane Survey (HiGAL) and
millimetre spectral line data from the Millimetre Astronomy Legacy Team 90 GHz
Survey (MALT90) to determine their global physical and kinematic structure. We
derive their masses, dust temperatures and radii and use virial analysis to
conclude that they are all likely gravitationally bound -- confirming that they
are likely YMC progenitors. We then compare the density profiles of these
clouds to those of the gas and stellar components of the Sagittarius B2 Main
and North proto-clusters and the stellar distribution of the Arches YMC. We
find that even in these clouds -- the most massive and dense quiescent clouds
in the Galaxy -- the gas is not compact enough to form an Arches-like ($M$ =
2x10$^{4}$ M$_{\odot}$, R$_{eff}$ = 0.4 pc) stellar distribution. Further
dynamical processes would be required to condense the resultant population,
indicating that the mass becomes more centrally concentrated as the
(proto)-cluster evolves. These results suggest that YMC formation may proceed
hierarchically rather than through monolithic collapse.
