Astronomical transients, such as supernovae and other rare stellar explosions, have been instrumental in some of the most significant discoveries in astronomy. New astronomical sky surveys will soon record unprecedented numbers of transients as sparsely and irregularly sampled multivariate time series. To improve our understanding of the physical mechanisms of transients and their progenitor systems, early-time measurements are necessary. Prioritizing the follow-up of transients based on their age along with their class is crucial for new surveys. To meet this demand, we present the first method of predicting the age of transients in real-time from multi-wavelength time-series observations. We build a Bayesian probabilistic recurrent neural network. Our method can accurately predict the age of a transient with robust uncertainties as soon as it is initially triggered by a survey telescope. This work will be essential for the advancement of our understanding of the numerous young transients being detected by ongoing and upcoming astronomical surveys.