  We demonstrate that the observationally inferred rapid onset of star
formation after parental molecular clouds have assembled can be achieved by
flow-driven cloud formation of atomic gas, using our previous three-dimensional
numerical simulations. We post-process these simulations to approximate CO
formation, which allows us to investigate the times at which CO becomes
abundant relative to the onset of cloud collapse. We find that global gravity
in a finite cloud has two crucial effects on cloud evolution. (a) Lateral
collapse (perpendicular to the flows sweeping up the cloud) leads to rapidly
increasing column densities above the accumulation from the one-dimensional
flow. This in turn allows fast formation of CO, allowing the molecular cloud to
``appear'' rapidly. (b) Global gravity is required to drive the dense gas to
the high pressures necessary to form solar-mass cores, in support of recent
analytical models of cloud fragmentation. While the clouds still appear
``supersonically turbulent'', this turbulence is relegated to playing a
secondary role, in that it is to some extent a consequence of gravitational
forces.
