A specific model is presented in which the Big Bang---a catastrophic cosmological event setting the beginning of observable time---is envisaged as due to the collision of two D-banes. During their bouncing back, open strings stretched between the two moving branes induce a departure from string criticality, thus providing Cosmological Inflation driven by the activated Liouville field, which is "dormant" in critical strings. WMAP and other data on fluctuations in the Cosmic Microwave Background Radiation fix the parameters of the model, such as the relative separation and velocity of the D-branes, in a natural way. The model also suggests a late Cosmological Acceleration Era, rooted in the "beginning", with a small, relaxation component in the present vacuum energy that may accomodate the breaking of Supersymmetry. In this picture, since observable time (of quantum origin) starts ticking after the collision, questions about the specific configuration of the brane worlds or how they started to move are merely philosophical or metaphysical.