  Dry, freely evolving granular materials in a dilute gaseous state coalesce
into dense clusters only due to dissipative interactions. This clustering
transition is important for a number of problems ranging from geophysics to
cosmology. Here we show that the evolution of a dilute, freely cooling granular
gas is determined in a universal way by the ratio of inertial flow and thermal
velocities, that is, the Mach number. Theoretical calculations and direct
numerical simulations of the granular Navier--Stokes equations show that
irrespective of the coefficient of restitution, density or initial velocity
distribution, the density fluctuations follow a universal quadratic dependence
on the system's Mach number. We find that the clustering exhibits a scale-free
dynamics but the clustered state becomes observable when the Mach number is
approximately of $\mathcal{O}(1)$. Our results provide a method to determine
the age of a granular gas and predict the macroscopic appearance of clusters.
