We report an implicit-solvent coarse-grained (CG) model for a water-soluble 1,3,5-benzenetricarboxamide (BTA) supramolecular polymer. The technical advances guaranteed by this CG model allow simulation of the self-assembly of 1000 BTA monomers and easy variation of the BTA concentration into the system down to experimental dilute conditions. In this way, we can monitor the mechanism of supramolecular polymerization as a function of the concentration at submolecular resolution exceeding the microsecond time scale. While increasing the concentration produces rapid formation of large disordered clusters that are then converted into BTA fibers, moving to very dilute concentrations favors early ordering of the oligomers in solution even at small sizes. Interestingly, we observe that below a certain concentration the oligomers that dynamically grow in solution during the self-assembly present the same level (and amplification) of order of prestacked equilibrated oligomers of the same size, meaning that concentration-dependent kinetic effects have disappeared from the polymerization mechanism.