  By [arXiv:1604.00528], a list of possible holonomy algebras for
pseudo-Riemannian manifolds with an indecomposable torsion free ${\rm
G}_{2}^*$-structure is known. Here indecomposability means that the standard
representation of the algebra on ${\mathbb R}^{4,3}$ does not leave invariant
any proper non-degenerate subspace. The dimension of the socle of this
representation is called the type of the Lie algebra. It is equal to one, two
or three. In the present paper, we use Cartan's theory of exterior differential
systems to show that all Lie algebras of Type I from the list in
[arXiv:1604.00528] can indeed be realised as the holonomy of a local metric.
All these Lie algebras are contained in the maximal parabolic subalgebra
$\mathfrak p_1$ that stabilises one isotropic line of ${\mathbb R}^{4,3}$. In
particular, we realise $\mathfrak p_1$ by a local metric.
