Collisionless shocks are key processes in astrophysics where the energy dissipation at the shock front is provided by collective plasma effects rather than particle collisions. While numerous simulations and laser-plasma experiments have shown they can result from the encounter of two plasma shells, a first principle theory of the shock formation is still lacking. In this respect, a series of 2D Particle-In-Cells simulations have been performed of two identical cold colliding pair plasmas. The simplicity of this system allows for an accurate analytical tracking of the physics. To start with, the Weibel-filamentation instability is triggered in the overlapping region, which generates a turbulent region after a saturation time τs. The incoming flow then piles-up in this region, building-up the shock density region according to some nonlinear processes, which will be the subject of future works. By evaluating the seed field giving rise to the instability, we derive an analytical expression for τs in good agreement with simulations. In view of the importance of the filamentation instability, we show a static magnetic field can cancel it if and only if it is perfectly aligned with the flow.