Classical explanation of Olber's paradox is, the dark matter between stars prohibits us to see the light of stars filling whole night sky. Such explanation is relevant for most distant active gallactic nuclei (AGN), observable only in infrared due the dust cover (so called the spherical dust galaxies revealed by Spitzer infrared telescope).
If we consider the finite speed of light, then the fact night sky is black would mean, the Universe can be larger, then the finite speed of light allows. Big Bang theory considers, light emanated by primordial matter was of very high frequency, therefore it can be observed as a CMB by now. If we consider cosmological principle of uniform isotropic universe, then the presence of CMB supports rather idea of infinitely large Universe, from which only the visible portion of light can be perceived. Radiofrequency part of CMB is forming a thermal noise of matter at the zero temperature (ZPE). As we can see, Olber's paradox cannot be used as an evidence of finite Universe and Big Bang theory reliably. AWT is assuming, observable Universe generation appears like rather common AGN from outer perspective, therefore our Universe doesn't differs very much from another quasars (white holes), which are observable inside of our Universe by Copernican principle.