  Let $G$ be a non-compact simple Lie group with Lie algebra $\mathfrak{g}$.
Denote with $m(\mathfrak{g})$ the dimension of the smallest non-trivial
$\mathfrak{g}$-module with an invariant non-degenerate symmetric bilinear form.
For an irreducible finite volume pseudo-Riemannian analytic manifold $M$ it is
observed that $\dim(M) \geq \dim(G) + m(\mathfrak{g})$ when $M$ admits an
isometric $G$-action with a dense orbit. The Main Theorem considers the case $G
= \widetilde{\mathrm{SO}}_0(p,q)$ providing an explicit description of $M$ when
the bound is achieved. In such case, $M$ is (up to a finite covering) the
quotient by a lattice of either $\widetilde{\mathrm{SO}}_0(p+1,q)$ or
$\widetilde{\mathrm{SO}}_0(p,q+1)$.
