Is the universal triangle free graph pseudofinite?

• A graph $G$ omits a graph $H$ if $H$ is not isomorphic to any subgraph of $G$. Note that this is weaker than requiring that $H$ is not isomorphic to any minor of $G$.
• For any $n > 2$, the Henson graph $\mathcal{H}_n$ denotes the universal $K_n$-free graph, i.e. the unique-up-to-isomorphism countable graph which omits $K_n$ and into which every countable graph omitting $K_n$ embeds.
• A structure $A$ is pseudofinite if every first order sentence that it satisfies is also satisfied by some finite structure in the same signature. Equivalently, $A$ is elementarily equivalent to an ultraproduct of finite structures.

The Henson graphs were introduced in [Hen71]. This question is also considered an important open question in combinatorics.