  We derive an upper bound on the waiting time for a variational weak solution
to Inverse Mean Curvature Flow in $\mathbb{R}^{n+1}$ to become star-shaped. As
a consequence, we demonstrate that any connected surface moving by the flow
which is not initially a topological sphere develops a singularity or
self-intersection within a prescribed time interval depending only on initial
data. Finally, we establish the existence of either finite-time singularities
or intersections for certain topological spheres under IMCF.
