Despite the importance for cellular processes, the dynamics of molecular assembly, especially on fast time scales, is not yet fully understood. To this end, we present a multi-layer microfluidic device and combine it with fluorescence fluctuation spectroscopy. We apply this innovative combination of methods to investigate the early steps in assembly of vimentin intermediate filaments (IFs). These filaments, together with actin filaments and microtubules, constitute the cytoskeleton of cells of mesenchymal origin and greatly influence their mechanical properties. We are able to directly follow the two-step assembly process of vimentin IFs and quantify the time scale of the first lateral step to tens of ms with a lag time of below 3 ms. Although demonstrated for a specific biomolecular system here, our method may potentially be employed for a wide range of fast molecular reactions in biological or, more generally, soft matter systems, as it allows for a precise quantification of the kinetics underlying the aggregation and assembly.