Is There a Smooth Approximation to Classifying Spaces $BG\,?$

Question

If you look at https://en.wikipedia.org/wiki/Chern%E2%80%93Weil_homomorphism, right above contents the claim is made that we can approximate the classifying space by smooth manifolds. I am aware of at least two constructions of the classifying space of a Lie group $G:$ one is Milnor's join construction, the other is via the geometric realization of the nerve of $G\,.$ Both of these involve taking a direct limit, therefore one can perform analogous constructions for a finite number $j\,,$ and I assume this gives $B_jG\,.$ Is there a reference for this?