  Nonequilibrium many-body dynamics is becoming one of the central topics of
modern condensed matter physics. Floquet topological states were suggested to
emerge in photodressed band structures in the presence of periodic laser
driving. Here we propose a viable nonequilibrium route without requiring
coherent Floquet states to reach the elusive magnetic Weyl semimetallic phase
in pyrochlore iridates by ultrafast modification of the effective
electron-electron interaction with short laser pulses. Combining \textit{ab
initio} calculations for a time-dependent self-consistent reduced Hubbard $U$
controlled by laser intensity and nonequilibrium magnetism simulations for
quantum quenches, we find dynamically modified magnetic order giving rise to
transiently emerging Weyl cones that are probed by time- and angle-resolved
photoemission spectroscopy. Our work offers a unique and realistic pathway for
nonequilibrium materials engineering beyond Floquet physics to create and
sustain Weyl semimetals. This may lead to ultrafast, tens-of-femtoseconds
switching protocols for light-engineered Berry curvature in combination with
ultrafast magnetism.
