  We investigate the consequences of introducing non-uniform initial conditions
in the dynamics of spin ensembles characterized by all-to-all interactions.
Specifically, our study involves the preparation of a set of semi-classical
spin ensembles with varying orientations. Through this setup, we explore the
influence of such non-uniform initial states on the disruption of permutational
invariance. Comparing this approach to the traditional scenario of initializing
with spins uniformly aligned, we find that the dynamics of the spin ensemble
now spans a more expansive effective Hilbert space. This enlargement arises due
to the inclusion of off-diagonal coherences between distinct total angular
momentum subspaces - an aspect typically absent in conventional treatments of
all-to-all spin dynamics. Conceptually, the dynamic evolution can be understood
as a composite of multiple homogeneous sub-ensembles navigating through
constrained subspaces. Notably, observables that are sensitive to the
non-uniformity of initial conditions exhibit discernible signatures of these
off-diagonal coherences. We adopt this fresh perspective to reexamine the
relaxation phenomena exhibited by the Dicke model, as well as a prototypical
example of a boundary time crystal. Intriguingly, ensembles initialized with
inhomogeneous initial conditions can show distinctive behaviors when contrasted
with canonical instances of collective dynamics. These behaviors encompass the
emergence of novel gapless excitations, the manifestation of limit-cycles
featuring dressed frequencies due to superradiance, instances of frequency
locking or beating synchronizations, and even the introduction of ``extra''
dimensions within the dynamics. In closing, we provide a brief overview of the
potential implications of our findings in the context of modern cavity quantum
electrodynamics (QED) platforms.
