We demonstrate the possibility of probing for the first time the fully nonperturbative regime of quantum electrodynamics. By using tightly compressed and focused electron beams in a 100 GeV-class particle collider, beamstrahlung radiation losses can be mitigated, allowing the particles to experience extreme electromagnetic fields. Three-dimensional particle-in-cell simulations confirm the viability of this approach. The experimental forefront envisaged has the potential to establish a novel research field and to stimulate the development of a new theoretical methodology for this yet unexplored regime of strong-field quantum electrodynamics.