Recent discovery of billions of habitable planets within the Milky Way alone and a practical route to nuclear fusion using Project PACER approach, suggesting that any habitable planet with intelligent life should be able to expand beyond their home planet and colonize the galaxy within a relatively short time. Given the absence of detection by SETI for the past few decades, we take this result for granted that no other industrial civilization exists within the galaxy and validated the rare earth and rare intelligence hypothesis by using rigorous astronomical and geological filter to reduce the potential candidate pool to host civilization < 1 per galaxy. So that, the total number of habitable extraterrestrial planets within the Milky Way capable of supporting advanced, intelligent life within the next 500 Myr is < 969. Most of which are earth-like orbiting around a single star with mass ranges from 0.712 to 1 solar mass. No exomoons are capable of supporting advanced life, and a negligible number of low mass binary systems (<0.712 solar mass) are habitable. Among these habitable, the emergence of intelligence is still rare and must be a relatively recent phenomena. Abstract By specifying species as a combination and permutation of traits acquired through evolutionary time, multi-nominal distribution profile of species can be constructed. Those with fewer traits are the most common. A particular multi-nominal distribution is build to model the emergence of civilization by specifying homo sapiens as an outlier. The deviation is calculated based on known cranial capacity of homo sapiens and the explosive growth of angiosperm. The multi-nominal distribution is then transformed/approximated into a more manipulative, generalized multivariate time-dependent exponential lognormal distribution to model biological evolution from the perspective of man. Abstract Most surprisingly, given that the emergence chance of civilization decreases exponentially into the past, predicted by the distribution model, a wall of semi-invisibility exists due to relativistic time delay of signal arrival at cosmological distance so that the universe appears empty even if a significant portion of the space could have already been occupied. The nearest extraterrestrial industrial civilization lies at least 51.85 million light years away, and possibly at least 100 million light years or beyond. Based on the starting model, no extraterrestrial civilization arises before 119 Mya within the observable universe, and no extraterrestrial civilization arises before 138 Mya within the universe by co-moving distance. Despite great distances between the nearest civilizations and the low probability of emergence within our vicinity, given the sheer size of the universe, the total number of intelligent extraterrestrial civilizations likely approaches infinity or \left(\frac{1}{4.4\cdot10^{7}}\right)^{3}\cdot3.621\cdot10^{6}\cdot10^{10^{10^{122}}} if the universe is finitely bounded. Based on incentives for economic growth and assuming wormhole shortens cosmic distances, all civilizations tend to expands near the speed of light and will eventually universally connect with each other via wormhole networks. Within such a network, the farthermost distances traversable from earth can be either infinite or 3.621\cdot10^{6}\cdot10^{10^{10^{122}}}light years in radius if the universe is finitely bounded. Abstract This work distinguishes from and enhances previous works on SETI by focusing on the biological and statistical aspect of the evolution of intelligence, statistical distributions can serve as indispensable tools for SETI to model the pattern and behavior of civilization's emergence and development and bridging the inter-disciplinary gap between astrophysical, biological, and social aspects of extraterrestrial study.