Neuronal transmitters are released from nerve terminals via the fusion of synaptic vesicles with the presynaptic membrane. Vesicles are attached to the membrane via the SNARE complex, comprising the vesicle associated protein synaptobrevin (Syb), the membrane associated protein syntaxin (Syx), and the cytosolic protein SNAP25, that together form a four-helical bundle. The full assembly of Syb onto the core SNARE bundle promotes vesicle fusion. We investigated SNARE assembly using a coarse-grained model of the SNARE complex that retains chemical specificity. Steered force-control simulations of SNARE unzippering were used to set up initial disassembled states of the SNARE complex. From these states, the assembly process was simulated. We find that if Syb is in helical form and proximal to the other helices, then the SNARE complex assembles rapidly, on a microsecond time-scale, which is well within in vivo synaptic vesicle fusion time scales. Assembly times grow exponentially with a separation distance between Syb and Syx C-termini. Our results indicate that for biologically relevant rapid assembly of the SNARE complex, Syb should be in helical form, and the SNARE constituent helices brought into proximity, possibly by an agent, such as a chaperone.