We review what has recently been learned from starburst-driven superwinds, galaxy-scale outflows, dwarf galaxy surveys, and evidence for early-universe merging scenarios. We apply this knowledge to simplified model populations of dwarf galaxies in the primeval galaxy era to demonstrate how a substantial fraction of the intergalactic medium can be permeated with magnetic fields by dwarf galaxy outflow winds in the volcanic early Mechanisms of both magnetic field regeneration and diffusion are discussed as they apply to galaxies at both primeval and later epochs of the universe. We propose that, in the past, magnetic field strengths in outflow superbubbles and halos were stronger than those now prevailing in the disks of current-epoch galaxies such as the Milky Way. We also show how subsequent acausal diffusion of magnetic fields (which we have not modeled) can propagate the fields over great distances in the universe within a Hubble time. We conclude that dwarf galaxies can effectively seed the intergalactic medium with magnetic fields for a wide range of outflow and galaxy density parameters. If the first galaxies form at or before z~10 in a bottom-up hierarchical merging scenario, a substantial fraction of the intergalactic medium will become permeated with a magnetic field at the present epoch. This intergalactic field seeding is largely accomplished by z~6.