In the context of quantum electrodynamics, a strong electric field can trigger the production of particle-antiparticle pairs, a phenomenon known as the Schwinger effect. In practical experimental scenarios, producing a pair requires quantum tunneling of particles over a long distance, thus suppressing the production rate and making this process very challenging to observe. Here we report an experimental investigation, in a cold-atom quantum simulator, of the effect of the external background field on pair production from the infinite-mass vacuum in a 1+1D U(1) lattice gauge theory in its quantum link model formulation, which we address through a genuine out-of-equilibrium protocol. The ability to tune the background field allows us to study pair production in a favorable regime of a large production rate. Furthermore, we probe the time evolution of the model in the zero fermion mass limit. We find that the energy spectrum of the time-evolved observables displays excitation peaks analogous to the (massive) bosonic modes of the Schwinger model, and whose phenomenology can be interpreted as a string inversion mechanism. Our work opens the door to quantum-simulation experiments that can controllably tune the production of pairs and manipulate their far-from-equilibrium dynamics.