  Young massive clusters (YMCs) have central stellar mass surface densities
exceeding $10^{4} M_{\odot} pc^{-2}$. It is currently unknown whether the stars
formed at such high (proto)stellar densities. We compile a sample of gas clouds
in the Galaxy which have sufficient gas mass within a radius of a few parsecs
to form a YMC, and compare their radial gas mass distributions to the stellar
mass distribution of Galactic YMCs. We find that the gas in the progenitor
clouds is distributed differently than the stars in YMCs. The mass surface
density profiles of the gas clouds are generally shallower than the stellar
mass surface density profiles of the YMCs, which are characterised by prominent
dense core regions with radii ~ 0.1 pc, followed by a power-law tail. On the
scale of YMC core radii, we find that there are no known clouds with
significantly more mass in their central regions when compared to Galactic
YMCs. Additionally, we find that models in which stars form from very dense
initial conditions require surface densities that are generally higher than
those seen in the known candidate YMC progenitor clouds. Our results show that
the quiescent, less evolved clouds contain less mass in their central regions
than in the highly star-forming clouds. This suggests an evolutionary trend in
which clouds continue to accumulate mass towards their centres after the onset
of star formation. We conclude that a conveyor-belt scenario for YMC formation
is consistent with the current sample of Galactic YMCs and their progenitor
clouds.
