  Our goal in this paper is to initiate the rigorous investigation of wave
turbulence and derivation of wave kinetic equations (WKE) for water waves
models. This problem has received intense attention in recent years in the
context of semilinear models, such as semilinear Schr\"odinger equations or
multi-dimensional KdV-type equations. However, our situation here is different
since the water waves equations are quasilinear and the solutions cannot be
constructed by iteration of the Duhamel formula due to unavoidable derivative
loss. This is the first of two papers in which we design a new strategy to
address this issue, in the context of 2D gravity waves.
