  We develop a nonperturbative theory for hole dynamics in antiferromagnetic
spin lattices, as described by the $t$-$J$ model. This is achieved by
generalizing the selfconsistent Born approximation to nonequilibrium systems,
making it possible to calculate the full time-dependent many-body wave
function. Our approach reveals three distinct dynamical regimes, ultimately
leading to the formation of magnetic polarons. Following the initial ballistic
stage of the hole dynamics, coherent formation of string excitations gives rise
to characteristic oscillations in the hole density. Their damping eventually
leaves behind magnetic polarons that undergo ballistic motion with a greatly
reduced velocity. The developed theory provides a rigorous framework for
understanding nonequilibrium physics of defects in quantum magnets and
quantitatively explains recent observations from cold-atom quantum simulations
in the strong coupling regime.
