Aims. We want to find the distribution of initial conditions that best reproduces disc observations at the population level. Methods. We first ran a parameter study using a 1D model that includes the viscous evolution of a gas disc, dust, and pebbles, coupled with an emission model to compute the millimetre flux observable with ALMA. This was used to train a machine learning surrogate model that can compute the relevant quantity for comparison with observations in seconds. This surrogate model was used to perform parameter studies and synthetic disc populations. Results. Performing a parameter study, we find that internal photoevaporation leads to a lower dependency of disc lifetime on stellar mass than external photoevaporation. This dependence should be investigated in the future. Performing population synthesis, we find that under the combined losses of internal and external photoevaporation, discs are too short lived. Conclusions. To match observational constraints, future models of disc evolution need to include one or a combination of the following processes: infall of material to replenish the discs, shielding of the disc from internal photoevaporation due to magnetically driven disc winds, and extinction of external high-energy radiation. Nevertheless, disc properties in low-external-photoevaporation regions can be reproduced by having more massive and compact discs. Here, the optimum values of the α viscosity parameter lie between 3 × 10−4 and 10−3 and with internal photoevaporation being the main mode of disc dispersal.