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In the field of Astrobiology, the precise location, prevalence and age of potential extraterrestrial intelligence (ETI) have not been explicitly explored. Here, we address these inquiries using an empirical galactic simulation model to analyze the spatial-temporal variations and the prevalence of potential ETI within the Galaxy. This model estimates the occurrence of ETI, providing guidance on where to look for intelligent life in the Search for ETI (SETI) with a set of criteria, including well-established astrophysical properties of the Milky Way. Further, typically overlooked factors such as the process of abiogenesis, different evolutionary timescales and potential self-annihilation are incorporated to explore the growth propensity of ETI. We examine three major parameters: 1) the likelihood rate of abiogenesis (λA); 2) evolutionary timescales (Tevo); and 3) probability of self-annihilation of complex life (Pann). We found Pann to be the most influential parameter determining the quantity and age of galactic intelligent life. Our model simulation also identified a peak location for ETI at an annular region approximately 4 kpc from the Galactic center around 8 billion years (Gyrs), with complex life decreasing temporally and spatially from the peak point, asserting a high likelihood of intelligent life in the galactic inner disk. The simulated age distributions also suggest that most of the intelligent life in our galaxy are young, thus making observation or detection difficult.