  Previously work of the author with Meier and Starkston showed that every
closed symplectic manifold $(X,\omega)$ with a rational symplectic form admits
a trisection compatible with the symplectic topology. In this paper, we
describe the converse direction and give explicit criteria on a trisection of a
closed, smooth 4-manifold $X$ that allows one to construct a symplectic
structure on $X$. Combined, these give a new characterization of 4-manifolds
that admit symplectic structures. This construction motivates several problems
on taut foliations, the Thurston norm and contact geometry in 3-dimensions by
connecting them to questions about the existence, classification and uniqueness
of symplectic structures on 4-manifolds.
