Are NP problems lower bounded by exponential order of growth?


My understanding of P. vs NP is quite limited. I can understand P refers to an algorithm with an upper bound (big O) with order of growth $ n^c$ for some constant c and variable n. My question is, do NP problems have a hypothesized lower bound order of growth (big Omega) of $ c^n$ for deterministic machines? I can’t find this stated anywhere and I’m trying to understand if this is something that is assumed or not.

Thanks.