If $u_n\rightharpoonup u$ in $L^2(0,T;L^2(\Omega))$. Can we find a subsequence such that $u_{n_k}(t)\rightharpoonup u(t)$ almost everywhere on $[0,T]$?

I'm not sure if this question is trivial or not, and how to even start! Any hints would be great!

I would add that $\Omega$ is a bounded open subset of $\mathbb{R}^n$.