Let's say we have a game where we should discover a number of length n, generated by RNG. If someone says us a solution it is easy to verify - we enter the number into machine and it compares it to the generated number (O(n)). On the other hand, it should be obvious, that to find the solution in general case takes exponential time - there is no way to discover a random number in polynomial time without any information. So, it should be a NP problem that is not in P
What I miss here?
It all hinges on what you mean by "RNG." You haven't been very clear on whether you mean a pseudorandom number generator, and in your second sentence it's not clear at which point you're talking about a seed for the PRNG and at which point you're talking about a value generated from a seed.
But if you clean up the argument a bit, this is roughly a version of the argument that the existence of one-way functions (functions easy to compute but hard to invert on random outputs) would imply $P \neq NP$. Naturally, this means that the existence of one-way functions is an open problem; in other words, nobody knows if it's possible to write down an RNG which is "random enough" to make this argument work. So the part where you say "it should be obvious" - it's not at all obvious! ("Obvious" and "clearly" are very dangerous words to allow yourself to use in proofs!)