  We present an approach for the calculation of the $\mathbb{Z}_2$ topological
invariant in non-crystalline two-dimensional quantum spin Hall insulators.
While topological invariants were originally mathematically introduced for
crystalline periodic systems, and crucially hinge on tracking the evolution of
occupied states through the Brillouin zone, the introduction of disorder or
dynamical effects can break the translational symmetry and imply the use of
larger simulation cells, where the $\bf{k}$-point sampling is typically reduced
to the single $\Gamma$-point. Here, we introduce a single-point formula for the
spin Chern number that enables to adopt the supercell framework, where a single
Hamiltonian diagonalisation is performed. Inspired by the work of E. Prodan
[Phys. Rev. B, $\textbf{80}$, 12 (2009)], our single-point approach allows to
calculate the spin Chern number even when the spin operator $\hat{s}_z$ does
not commute with the Hamiltonian, as in the presence of Rashba spin-orbit
coupling. We validate our method on the Kane-Mele model, both pristine and in
the presence of Anderson disorder. Finally, we investigate the disorder-driven
transition from the trivial phase to the topological state known as topological
Anderson insulator. Beyond disordered systems, our approach is particularly
useful to investigate the role of defects, to study topological alloys and in
the context of ab-initio molecular dynamics simulations at finite temperature.
