Show that $\mathbb{P}(\tau<\infty)=1$ where $\tau:=\inf \{n\geq 1\::\:|S_{n}|=N \}$ and $\{S_{n}\}$ is a symmetric Random Walk in $\mathbb{Z}$

Question

Let $\{S_{n}:n\geq 0\}$ be a symmetric Random Walk in $\mathbb{Z}$ with $S_{0}=0$, that is, $S_{n}=X_{1}+\ldots+X_{n}$ for $n\geq 1$ where $\{X_{k}\}_{k=1}^{\infty}$ iid with $\mathbb{P}(X_{k}=-1)=\frac{1}{2}=\mathbb{P}(X_{k}=1)$.

We consider the stopping time $$\tau:=\inf \{n\geq 1\::\:|S_{n}|=N \}.$$

Show that $\mathbb{P}(\tau<\infty)=1$.