The epoch in which galactic discs settle is a major benchmark for testing models of galaxy formation and evolution but remains largely unknown. Once discs settle and become sufficiently self-gravitating, stellar bars are able to form; therefore, determining the ages of bars can shed light on the epoch of disc settling, and on the onset of secular evolution. Nevertheless, timing when the bar formed has proven challenging. In this work we present a new methodology for obtaining the bar age, using the star formation history of nuclear discs. Nuclear discs are rotation-supported structures, built by gas pushed to the centre via bar-induced torques, and their formation is thus coincident with bar formation. In particular, we used integral field spectroscopic data from the TIMER survey to disentangle the star formation history of the nuclear disc from that of the underlying main disc, which enables us to more accurately determine when the nuclear disc formed. We demonstrate the methodology on the galaxy NGC 1433 - which we find to host an old bar that is 7.5−1.1+1.6(sys)−0.5+0.2(stat) Gyr old - and describe a number of tests carried out on both the observational data and numerical simulations. In addition, we present evidence that the nuclear disc of NGC 1433 grows in accordance with an inside-out formation scenario. This methodology is applicable to high-resolution integral field spectroscopic data of barred galaxies with nuclear discs, making it ideally suited for the TIMER survey sample. In the future we will thus be able to determine the bar age for a large sample of galaxies, shedding light on the epoch of disc settling and bar formation.