This study presents a thermomechanical processing concept which is capable of exploiting the full industrial application potential of recently introduced AlMgZn(Cu) alloys. The beneficial linkage of alloy design and processing allows not only to satisfy the long-standing trade-off between high mechanical strength in use and good formability during processing but also addresses the need for economically feasible processing times. After an only 3-hour short pre-aging treatment at 100°C, the two investigated alloys, based on commercial EN AW-5182 and modified with additions of Zn and Zn+Cu respectively, show high formability due to increased work-hardening. Then, these alloys exhibit a giant hardening response of up to 184 MPa to reach a yield strength of 410 MPa after a 20-minute short final heat treatment at 185°C, i.e. paint-baking. This rapid hardening response strongly depends on the number density, size distribution and constitution of precursors acting as preferential nucleation sites for T-phase precursor precipitation during the final high-temperature aging treatment and is significantly increased by the addition of Cu. Minor deformation (2%) after pre-aging and before final heat treatment further enhances the development of hardening precipitates additionally by activating dislocation-supported nucleation and growth. Tensile testing, quantitative and analytical electron-microscopy methods, atom probe analysis and DFT calculations were used to characterize the alloys investigated in this work over the thermomechanical processing route. The influence of pre-strain on the hardening response and the role of Cu additions in early-stage cluster nucleation are discussed in detail and supported by in-situ STEM experiments and first-principles calculations.