The formation of persistent slip bands (PSBs) at early stages of fatigue plays an important role in fatigue damage. In order to get a better understanding of the physics involved at the dislocation scale, 3D discrete dislocation dynamic simulations are set up in the case of an isolated surface grain of Cu cyclically loaded in single slip. Simulations reveal the complex transformation process of the dislocation microstructure from a homogeneous distribution into an organized microstructure made of slip bands mainly composed of dislocation dipoles and prismatic loops. These slip bands are the embryo of the PSBs observed for large number of cycles. The localization mechanism evidenced by the simulations is well explained from a stress field analysis which highlights the role of cross-slip. A saturation regime is reached after a few cycles during which dislocation microstructure, dislocation densities and height of extrusions/intrusions remain unchanged. Furthermore, the linear relationship between the volume fraction of slip bands and the imposed plastic strain amplitude is retrieved by the simulations and the stability of the slip bands is verified by decreasing the plastic strain amplitude after the saturation regime is reached. Finally, when compared to AISI 316L stainless steel, Cu shows a tendency to build more bands with relatively larger thicknesses which is attributed to the differences in the cross-slip probability.