  Weinstein trisection is a trisection of a symplectic 4-manifold whose
1-handlebodies are the Weinstein domain for the symplectic structure induced
from an ambient manifold. Lambert-Cole, Meier, and Starkston showed that every
closed symplectic 4-manifold admits a Weinstein trisection. In this paper, we
construct a Weinstein trisection of $\Sigma_g\times \Sigma_h$. As a consequence
of this construction, we construct a little explicit Weinstein trisection of
$S^2\times S^2$.
