Collisionless shocks are a key ingredient of the Fireball scenario. Yet, their formation from the encounter of two collisionless plasma shells is not understood from first principles. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step towards a microscopic understanding of the process, we analyze here in details the initial instability phase. On the one hand, 2D relativistic PIC simulations are performed where two symmetric initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes with ω = 0+iδ govern the linear phase. We derive an expression for the duration of the linear phase in reasonable agreement with the simulations.