Achieving extreme deformations without electrical breakdown has been a longstanding challenge in the dielectric elastomer community. In this paper, we present a novel approach for accessing giant in-plane stretches in circular dielectric elastomer membranes by leveraging nonlinear dynamics, specifically short-duration voltage pulses. These voltage pulses—applied about nominal bias voltages where the large-stretch equilibrium does not experience dielectric breakdown—create transient stretches that, if sufficiently large, cause the membrane to dynamically snap-through to its large-stretch equilibrium. These giant deformations are reversible; pulsed voltage drops can return the membrane from its large-stretch equilibrium to its small-stretch equilibrium. Parametric analyses are used to determine the combinations of pulse amplitude and duration that result in snap-through. Corresponding through-thickness electric fields are shown to be below stretch-dependent dielectric strengths from the literature, suggesting practical feasibility. Unlike other techniques for accessing extreme stretches in dielectric elastomers, the present approach relies on voltage control alone; it therefore does not require altering the external mechanical forces that cause pre-stretch and can be applied without modifying the elastomer’s mechanical compliance. This research demonstrates that carefully designed voltage pulses may permit existing and emerging soft material technologies to access extreme, large-stretch equilibria without dielectric breakdown.