  We present a detailed comparison of the Milky Way (MW) globular cluster (GC)
kinematics with the 25 Milky Way-mass cosmological simulations from the
E-MOSAICS project. While the MW falls within the kinematic distribution of GCs
spanned by the simulations, the relative kinematics of its metal-rich
($[\rm{Fe/H}]>-1.2$) versus metal-poor ($[\rm{Fe/H}]<-1.2$), and inner
($r<8\rm{kpc}$) versus outer ($r>8\rm{kpc}$) populations are atypical for its
mass. To understand the origins of these features, we perform a comprehensive
statistical analysis of the simulations, and find 18 correlations describing
the assembly of $L^*$ galaxies and their dark matter haloes based on their GC
population kinematics. The correlations arise because the orbital distributions
of accreted and in-situ GCs depend on the masses and accretion redshifts of
accreted satellites, driven by the combined effects of dynamical fraction,
tidal stripping, and dynamical heating. Because the kinematics of
in-situ/accreted GCs are broadly traced by the metal-rich/metal-poor and
inner/outer populations, the observed GC kinematics are a sensitive probe of
galaxy assembly. We predict that relative to the population of $L^*$ galaxies,
the MW assembled its dark matter and stellar mass rapidly through a combination
of in-situ star formation, more than a dozen low-mass mergers, and $1.4\pm1.2$
early ($z=3.1\pm1.3$) major merger. The rapid assembly period ended early,
limiting the fraction of accreted stars. We conclude by providing detailed
quantitative predictions for the assembly history of the MW.
