We present three large classes of examples of conformal structures whose Fefferman–Graham ambient metrics can be found explicitly. Our method for constructing these examples rests upon a set of sufficiency conditions under which the Fefferman–Graham equations are assured to reduce to a system of inhomogeneous linear partial differential equations. Our examples include conformal pp-waves and, more importantly, conformal structures that are defined by generic co-rank $3$ distributions in dimensions $5$ and $6$. Our examples illustrate various aspects of the ambient metric construction.

The holonomy algebras of our ambient metrics are studied in detail. In particular, we exhibit a large class of metrics with holonomy equal to the exceptional non-compact Lie group $\operatorname{G}_2$ as well as ambient metrics with holonomy contained in $\operatorname{Spin}(4, 3)$.