  Young massive clusters (YMCs) are the most compact, high-mass stellar systems
still forming at the present day. The precursor clouds to such systems are,
however, rare due to their large initial gas mass reservoirs and rapid
dispersal timescales due to stellar feedback. Nonetheless, unlike their high-z
counterparts, these precursors are resolvable down to the sites of individually
forming stars, and hence represent the ideal environments in which to test the
current theories of star and cluster formation. Using high angular resolution
(1$^{\prime\prime}$ / 0.05pc) and sensitivity ALMA observations of two YMC
progenitor clouds in the Galactic Centre, we have identified a suite of
molecular line transitions -- e.g. c-C$_{3}$H$_{2} $($7-6$) -- that are
believed to be optically thin, and reliably trace the gas structure in the
highest density gas on star-forming core scales. We conduct a virial analysis
of the identified core and proto-cluster regions, and show that half of the
cores (5/10) and both proto-clusters are unstable to gravitational collapse.
This is the first kinematic evidence of global gravitational collapse in YMC
precursor clouds at such an early evolutionary stage. The implications are that
if these clouds are to form YMCs, then they likely do so via the
"conveyor-belt" mode, whereby stars continually form within dispersed dense gas
cores as the cloud undergoes global gravitational collapse. The concurrent
contraction of both the cluster-scale gas and embedded (proto)stars ultimately
leads to the high (proto)stellar density in YMCs.
