The existence of massive quiescent galaxies at high redshift seems to require rapid quenching, but it is unclear whether all quiescent galaxies have gone through this phase and what physical mechanisms are involved. To study rapid quenching, we use rest-frame colors to select 12 young quiescent galaxies at $z \sim 1.5$. From spectral energy distribution fitting, we find that they all experienced intense starbursts prior to rapid quenching. We confirm this with deep Magellan/FIRE spectroscopic observations for a subset of seven galaxies. Broad emission lines are detected for two galaxies and are most likely caused by AGN activity. The other five galaxies do not show any emission features, suggesting that gas has already been removed or depleted. Most of the rapidly quenched galaxies are more compact than normal quiescent galaxies, providing evidence for a central starburst in the recent past. We estimate an average transition time of $300\,\rm Myr$ for the rapid quenching phase. Approximately $4\%$ of quiescent galaxies at $z=1.5$ have gone through rapid quenching; this fraction increases to $23\%$ at $z=2.2$. We identify analogs in the TNG100 simulation and find that rapid quenching for these galaxies is driven by AGN, and for half of the cases, gas-rich major mergers seem to trigger the starburst. We conclude that these massive quiescent galaxies are not just rapidly quenched but also rapidly formed through a major starburst. We speculate that mergers drive gas inflow towards the central regions and grow supermassive black holes, leading to rapid quenching by AGN feedback.