The formation of stellar structures in galaxies is intimately connected to all evolutionary processes. Violent mergers prevent or destroy fragile discs, while minor mergers are able to promote the formation of classical bulges. Secular evolution favours the formation of bars, rings, nuclear discs, etc. The assembly history of stellar structures holds crucial information about the full lives of their hosts. We present the cosmic evolution of the mass growth of bulges and discs in a selection of 129 unbarred galaxies from the CALIFA survey. After separating both components through innovative spectrophotometric decompositions performed with the C2D code, we find a clear trend that more massive bulges, as well as bulges in more massive galaxies, assemble the majority of their stellar mass quicker than lower mass bulges or bulges in lower mass galaxies. Moreover, at least half of the bulge stellar mass is already in place at z ∼ 1 for all galaxies. Discs, on their side, form later than bulges, with a delay between the mass growth of bulges and discs that is dependent on galaxy mass. All our results point towards a Universe in which bulges act as seeds for galaxy formation, driving the properties of the discs that will be born later.