We report direct experimental evidence for a layer-dependent step-edge barrier in organic thin film growth, investigating di-indenoperylene on SiO_{2} as an archetypical system. In particular, we show that a noticeable Ehrlich-Schwöbel effect emerges only beyond the 3rd molecular layer, accompanied by mass step-upward diffusion. We further disclose that this thickness dependence of the interlayer transport is directly related to molecular reorientations during the first stages of the growth. This is ultimately responsible for a morphological transition from layer-by-layer growth to surface rapid roughening. These experimental findings should compel further development of molecular-scale models for organic thin film growth.