Nanostructured films obtained by the assembling of preformed atomic clusters are of strategic importance for a wide variety of applications. The deposition of clusters produced in the gas phase onto a substrate offers the possibility to control and engineer the structural and functional properties of the cluster-assembled films. To date the microscopic mechanisms underlying the growth and structuring of cluster-assembled films are poorly understood, and in particular the transition from the sub-monolayer to the thin film regime is experimentally unexplored. Here we report the systematic characterization by Atomic Force Microscopy of the evolution of the structural properties of cluster-assembled films deposited by Supersonic Cluster Beam Deposition. As a paradigm of nanostructured systems, we have focused our attention on cluster-assembled zirconia films, investigating the influence of the building blocks dimensions on the growth mechanisms and on the roughening of the thin films, following the growth process from the early stages of the sub-monolayer to the thin film regime. Our results demonstrate that the growth dynamics in the sub-monolayer regime determines different morphological properties of the cluster-assembled thin film. The evolution of roughness with the number of deposited clusters reproduces exactly the growth exponent of the ballistic deposition in the 2+1 model, from the sub-monolayer to the thin film regime.