This paper investigates by in situ high-resolution X-ray radiography and tomography the behavior of colloidal suspensions of alumina partic les during directional solidification by freezing. The combination of these techniques provided both qualitative and quantitative information about the propagation kinetic of the solid/liquid interface, the particle redistribution between the crystals and a particle-enriched phase, and the three-dimensional organization of the ice crystals. In this first part of two companion papers, the precursor phenomena leading to directional crystallization during the first instants of solidification are studied. Mullins-Sekerka instabilities are not necessary to explain the dynamic evolution of the interface pattern. Particle redistribution during these first instants is dependent on the type of crystals growing into the suspension. The insights gained into the mechanisms of solidification of colloidal suspensions may be valuable for the materials processing routes derived for this type of directional solidification (freeze-casting), and of general interest for those interested in the interactions between solidification fronts and inert particles.