Existence of proper isometry in some universal C*-algebra

Question

Consider the universal C$^\ast$-algebra $A_{\delta}$ for $\delta \in (0,1)$, generated by $\{1, u\}$ subject to the relation $$ \| 1 - u^\ast u \| \leq \delta .$$ I'm trying to prove the existence of a proper isometry $s \in A_\delta$, so an element $s$ for which $s^\ast s = 1$ and $ss^\ast \neq 1$. I think I will have to use the fact that $A_\delta$ has its universal property but I really don't see to which other C*algebra I must apply it.