We show that a pulsed stimulus can be used to generate many-body quantum coherences in light-matter systems of general size. Specifically, we calculate the exact time-evolution of an N qubit system coupled to a global boson field, in response to an up-down pulse. The pulse is chosen so that the system dynamically crosses the system's quantum phase transition on both the up and down portion of the cycle. We identify a novel form of dynamically-driven quantum coherence emerging for general N and without having to access the empirically challenging strong-coupling regime. Its properties depend on the speed of the changes in the stimulus. Non-classicalities arise within each subsystem that have eluded previous analyses. Our findings show robustness to losses and noise, and have potential functional implications at the systems level for a variety of nanosystems, including collections of N atoms, molecules, spins, or superconducting qubits in cavities—and possibly even vibration-enhanced light-harvesting processes in macromolecules.