Quantum phase transitions, transitions between many-body ground states, are of extensive interest in research ranging from condensed-matter physics to cosmology1,2,3,4. Key features of the phase transitions include a stage with rapidly growing new order, called inflation in cosmology5, followed by the formation of topological defects6,7,8. How inflation is initiated and evolves into topological defects remains a hot topic of debate. Ultracold atomic gas offers a pristine and tunable platform to investigate quantum critical dynamics9,10,11,12,13,14,15,16,17,18,19,20,21. We report the observation of coherent inflationary dynamics across a quantum critical point in driven Bose–Einstein condensates. The inflation manifests in the exponential growth of density waves and populations in well-resolved momentum states. After the inflation stage, extended coherent dynamics is evident in both real and momentum space. We present an intuitive description of the quantum critical dynamics in our system and demonstrate the essential role of phase fluctuations in the formation of topological defects.