Analytic estimates of the viscous time-scale due to cloud–cloud collisions have been as high as thousands of Gyr. Consequently, cloud collisions are widely ignored as a source of viscosity in galactic discs. However, capturing the hydrodynamics of discs in simple analytic models is a challenge, because of both the wide dynamic range and the importance of 2D and 3D effects. To test the validity of analytic models, we present estimates for the viscous time-scale that are measured from 3D smoothed particle hydrodynamics simulations of disc formation and evolution. We have deliberately removed uncertainties associated with star formation and feedback, thereby enabling us to place lower bounds on the time-scale for this process. We also contrast collapse simulations with results from simulations of initially stable discs and examine the impact of numerical parameters and assumptions on our work, to constrain possible systematics in our estimates. We find that cloud-collision viscous time-scales are in the range of 0.6–16 Gyr, considerably shorter than previously estimated. This large discrepancy can be understood in terms of how the efficiency of collisions is included in the analytical estimates. We find that the viscous time-scale only depends weakly on the number of clouds formed, and so while the viscous time-scale will increase with increasing resolution, this effect is too weak to alter our conclusions.