This nLab page defines (in Definition 2.6) a smooth $\infty$-groupoid as an $(\infty,1)$-sheaf on the $(\infty,1)$-category $C = \text{CartSp}_{\text{smooth}}$ whose objects are Cartesian spaces, arrows are smooth maps between them, 2-cells are smooth homotopies, and so on.
I assume this is with respect to an $(\infty,1)$-site structure on $C$.
However, the linked article above only seems to describe (in Definition 2.5) a site structure on the strict 1-category $C_{\leq1}$ of the ("1-strict") $(\infty,1)$-category $C$.
I was wondering, given the Grothendieck topology on $C_{\leq1}$, is there a "canonical" choice of $(\infty,1)$-Grothendieck topology on $C$? Is this being used implicitly in the above nLab page?