We report bond formation induced by an ultrashort UV pulse. The photochemical process is described by quantum dynamics as coherent electronic and nuclear motions during the ultrashort pulse induced ring closure of norbornadiene to quadricyclane. Norbornadiene consists of two ethylene moieties connected by a rigid (CH2)3 bridge. Upon photoexcitation, two new sigma bonds are formed, resulting in the closure of a four-atom ring. As a medium-sized polyatomic molecule, norbornadiene exhibits a high density of strongly coupled electronic states from about 6 eV above the ground state. We report on inducing the formation of the new bonds using a short femtosecond UV pulse to pump a non-equilibrium electronic density in the open form that evolves towards the closed ring form. As the coherent electronic-nuclear coupled dynamics unfold, the excited states change character through non-adiabatic interactions and become valence states for the two new C-C bonds of quadricyclane. Our three-dimensional fully quantum dynamical grid simulations during the first 200 fs show that short UV pulses of different polarization initiate markedly different initial non-equilibrium electronic densities that follow different dynamical paths to the S0/S1 conical intersection. They lead to different initial relative yields of quadricyclane, thereby opening the way to controlling bond-making with attopulses.