Existence of Pseudorandom Generator
If you choose $G$ from the uniform random distribution on $\{0, 1\}^n \to \{0, 1\}^{2^{\epsilon n}}$ without restrictions, then nothing can (correctly) distinguish between the uniform distribution and the output of $G$, because you made it uniformly random by definition. At this point the output of $G$ is no longer pseudo-random, it is random.