We present the first large-scale study that demonstrates how ages can be determined for large samples of stars through Galactic chemical evolution. Previous studies found that the elemental abundances of a star correlate directly with its age and metallicity. Using this knowledge, we derive ages for 214 577 stars in GALAH DR3 using only overall metallicities and chemical abundances. Stellar ages are estimated via the machine learning algorithm XGBoost for stars belonging to the Milky Way disc with metallicities in the range -1 < [Fe/H] < 0.5, using main-sequence turn-off stars as our training set. We find that stellar ages for the bulk of GALAH DR3 are precise to 1-2 Gyr using this method. With these ages, we replicate many recent results on the age-kinematic trends of the nearby disc, including the solar neighbourhood's age-velocity dispersion relationship and the larger global velocity dispersion relations of the disc found using Gaia and GALAH. These results show that chemical abundance variations at a given birth radius are small, and that strong chemical tagging of stars directly to birth clusters may prove difficult with our current elemental abundance precision. Our results highlight the need to measure abundances for as many nucleosynthetic production sites as possible in order to estimate reliable ages from chemistry. Our methods open a new door into studies of the kinematic structure and evolution of the disc, as ages may potentially be estimated to a precision of 1-2 Gyr for a large fraction of stars in existing spectroscopic surveys.