We have investigated the ordering dynamics and mechanism of a nearly symmetric polystyrene-bloch-polyisoprene by quenching the specimen from a temperature above the order-disorder transition temperature, T-ODT, to temperatures below T-ODT, by using time-resolved small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) as a function of quench depths. The time-resolved SAXS revealed that the ordering at shallow quenches proceeds via nucleation and growth process as follows : (I) after quenching the specimen, the thermal concentration fluctuations relax rapidly from the initial state to the disordered state at the temperature very close to T-ODT within the shortest time covered in this experiment; (II) the system stays in this disordered state for a certain incubation period; (III) after this period, the lamellar microdomains are nucleated and grow. This ordering mechanism is essentially same at any quench depths covered in this experiments, except for the largest quench depth. Furthermore the Avrami analysis together with TEM observations revealed that the nucleation occurs homogeneonsly and generates a highly anisotropic shape of grains composed of lamellae with their size parallel to lamellar normals being much greater than that normal to them.