Suppose $g:[0,\infty)\rightarrow [0,\infty)$ is a cotinuous increasing function with $g(0)=0$. Is it possible to find two constants $C>0$ and $q>0$ such that $$g(s)\geq Cs^q,\ \forall\ s\in [0,\delta)$$

where $\delta>0$ is an small number. 

Thank you.

Edit: Sorry, I forgot one hypothesis.