The brain consists of billions of neurons connected by ultra-dense synapses, showing remarkable efficiency, robust flexibility, and economy in information processing. It is generally believed that these advantageous properties are rooted in brain connectivity; however, direct evidence remains absent owing to technical limitations or theoretical vacancy. This research explores the origins of these properties in the largest yet brain connectome of the fruit fly. We reveal that functional connectivity formation in the brain can be explained by a percolation process controlled by synaptic excitation-inhibition (E/I) balance. By increasing the E/I balance gradually, we discover the emergence of these properties as byproducts of percolation transition when the E/I balance arrives at 3:7. As the E/I balance keeps increase, an optimal E/I balance 1:1 is unveiled to ensure these three properties simultaneously, consistent with previous in vitro experimental predictions. Once the E/I balance reaches over 3:2, an intrinsic limitation of these properties determined by static (anatomical) brain connectivity can be observed. Our work demonstrates that percolation, a universal characterization of critical phenomena and phase transitions, may serve as a window toward understanding the emergence of various brain properties.