Psuedorandom Generator Classification
NP contains decision problems. Problems with a yes or no answer. Finding $x$ such that $g(x) = y$ for some given pseudo-random generator $g$ and output $y$ isn't a decision problem. It's a function problem.
You can turn this into decision problem by asking whether the $i$'th bit of $x$ is 1 instead. Then you can still find $x$ by just asking this question once for every bit.
Now this problem of deciding on the $i$'th bit is trivially in NP. Speaking informally, every problem that has efficiently verifiable proofs is in NP. $x$ is just such a proof. You can quickly check it's $i$'th bit. And you can quickly check that $g(x) = y$.