Context. The properties of protoplanetary discs determine the conditions for planet formation. In addition, planets can already form during the early stages of infall. Aims. We constrain physical quantities such as the mass, radius, lifetime, and gravitational stability of protoplanetary discs by studying their evolution from formation to dispersal. Methods. We perform a population synthesis of protoplanetary discs with a total of 50 000 simulations using a 1D vertically integrated viscous evolution code, studying a parameter space of final stellar mass from 0.05 to 5 M_⊙. Each star-and-disc system is set up shortly after the formation of the protostar and fed by infalling material from the parent molecular cloud core. Initial conditions and infall locations are chosen based on the results from a radiation-hydrodynamic population synthesis of circumstellar discs. We also consider a different infall prescription based on a magnetohydrodynamic (MHD) collapse simulation in order to assess the influence of magnetic fields on disc formation. The duration of the infall phase is chosen to produce a stellar mass distribution in agreement with the observationally determined stellar initial mass function. Results. We find that protoplanetary discs are very massive early in their lives. When averaged over the entire stellar population, the discs have masses of ~0.3 and 0.1 M_⊙ for systems based on hydrodynamic or MHD initial conditions, respectively. In systems characterised by a final stellar mass ~1 M_⊙, we find disc masses of ~0.7 M_⊙ for the “hydro” case and ~0.2 M_⊙ for the “MHD” case at the end of the infall phase. Furthermore, the inferred total disc lifetimes are long, ≈5–7 Myr on average. This is despite our choice of a high value of 10⁻² for the background viscosity α-parameter. In addition, we find that fragmentation is common in systems that are simulated using hydrodynamic cloud collapse, with more fragments of larger mass formed in more massive systems. In contrast, if disc formation is limited by magnetic fields, fragmentation may be suppressed entirely. Conclusions. Our work draws a picture quite different from the one often assumed in planet formation studies: protoplanetary discs are more massive and live longer. This means that more mass is available for planet formation. Additionally, when fragmentation occurs, it can affect the disc’s evolution by transporting large amounts of mass radially. We suggest that the early phases in the lives of protoplanetary discs should be included in studies of planet formation. Furthermore, the evolution of the central star, including its accretion history, should be taken into account when comparing theoretical predictions of disc lifetimes with observations.