Photometric reverberation mapping can detect the radial extent of the accretion disc (AD) in Active Galactic Nuclei by measuring the time delays between light curves observed in different continuum bands. Quantifying the constraints on the efficiency and accuracy of the delay measurements is important for recovering the AD size-luminosity relation, and potentially using quasars as standard candles. We have explored the possibility of determining the AD size of quasars using next-generation Big Data surveys. We focus on the Legacy Survey of Space and Time (LSST) at the Vera C. Rubin Observatory, which will observe several thousand quasars with the Deep Drilling Fields and up to 10 million quasars for the main survey in six broadband filter during its 10-year operational lifetime. We have developed extensive simulations that take into account the characteristics of the LSST survey and the intrinsic properties of the quasars. The simulations are used to characterise the light curves from which AD sizes are determined using various algorithms. We find that the time delays can be recovered with an accuracy of 5 and 15% for light curves with a time sampling of 2 and 5 days, respectively. The results depend strongly on the redshift of the source and the relative contribution of the emission lines to the bandpasses. Assuming an optically thick and geometrically thin AD, the recovered time-delay spectrum is consistent with black hole masses derived with 30% uncertainty.