We perform drainage experiments of a linear alkane fluid (n-hexadecane) down to molecular thicknesses, and focus on the role played by the confinement rate. We show that molecular layering is strongly influenced by the velocity at which the confining walls are approached: under high enough shear rates, the confined medium behaves as a structureless liquid of enhanced viscosity for film thickness below $\sim$10 nm. Our results also lead us to conclude that a rapidly confined film can be quenched in a metastable disordered state, which might be related with recent intriguing results on the shear properties of confined films produced at different rates [Zhu and Granick, Phys. Rev. Lett. {\bf 93}, 096101 (2004)].