  We utilize a novel numerical technique to model star formation in
cosmological simulations of galaxy formation - called Superstars - to simulate
a Milky Way-like galaxy with $\gtrsim10^8$ star particles to study the
formation and evolution of out-of-equilibrium stellar disc structures in a full
cosmological setting. In the plane defined by the coordinate and velocity
perpendicular to the mid-plane (vertical phase space, $\{Z,V_Z\}$), stars in
Solar-like volumes at late times exhibit clear spirals qualitatively similar in
shape and amplitude to the $Gaia$ ``Snail shell'' phase spiral. We show that
the phase spiral forms at a look back time of $\sim 6$ Gyr during the
pericentric passage of a $\sim10^{10}$ $\rm M_{\odot}$ satellite on a polar
orbit. This satellite stimulates the formation of a resonant wake in the dark
matter halo while losing mass at a rate of $\sim0.5$-$1$ dex per orbit loop.
The peak magnitude of the wake-induced gravitational torque at the Solar radius
is $\sim 8$ times that from the satellite, and triggers the formation of a disc
warp that wraps up into a vertical phase spiral over time. As the wake decays,
the phase spiral propagates several Gigayears to present-day and can be
described as ``ever-present'' once stable disc evolution is established. These
results suggest an alternative scenario to explain the $Gaia$ phase spiral
which does not rely on a perturbation from bar buckling or a recent direct hit
from a satellite.
