How to prove existence of the language
Combine the following two facts:


$\mathsf{NTIME}(n) \subseteq \mathsf{TIME}(2^{O(n)})$, by deterministic simulation of nondeterminism.
$\mathsf{TIME}(2^{O(n)}) \subsetneq \mathsf{TIME}(2^{n^2})$, by the time hierarchy theorem.