2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35029We show how to prescribe the initial data of a characteristic problem satisfying the costraints, the smallness, the regularity and the asymptotic decay suitable to prove a global existence result. In this paper, the first of two, we show in detail the construction of the initial data and give a sketch of the existence result. This proof, which mimicks the analogous one for the non characteristic problem in [Kl-Ni], will be the content of a subsequent paper.77 pages, no figures; corrected misprints and minor errors, to appear on Journal of Hyperbolic Differential Equations (JHDE)General Relativity and Quantum Cosmologytext