A bound for the occupation time of a diffusion

Let $sigma: mathbb R times mathbb R to mathbb R$ be a Lipschitz continuous function bounded below by some $M > 0$.

Let $W$ be a standard Brownian motion, and let $X$ be the solution to the SDE

$$dX_t = sigma(t, X_t) dW_t$$

with $X_0 = 0$.

Fix $T > 0$. Does there exist, for every $varepsilon, h > 0$ a $delta > 0$ such that

$$mathbb Pleft(int_{0}^T mathbf 1_{(-delta, delta)} (X_s) ds > hright) < varepsilon?$$