Let $(M, \omega)$ be a symplectic 4-manifold. An immersed symplectic surface is an immersion $v: S \to M$ such that $v^*\omega>0$ is a volume form.
Fix a tame/compatible almost complex structure $J$. A holomorphic curve is a map $u:(\Sigma, j) \to (M, J)$ such that $$du+J\circ du \circ j=0.$$
If $u$ is an immersion holomorphic curve, then it is also an immersed symplectic surface. The reason is that $u^*\omega(\partial_x, \partial_y)=\omega(\partial_xu, \partial_yu)= \omega(\partial_xu, J\partial_xu)>0$, where $(x, y)$ are holomorphic coordinates on $\Sigma.$
Conversely, I want to ask given an immersed symplectic surface $v: S \to M$, can we find a tame/compatible almost complex structure $J$ such that $v$ is holomorphic?