We use time dependent density functional theory to study short-time dynamics of the screening of a negative charge suddenly introduced in a free electron gas. The electron gas is modeled with a finite-size jellium cluster. We find that the screening is built-up locally on a time scale well below the femtosecond for typical metallic densities. At this ultrashort time scale, the time evolution is not affected by the cluster boundary conditions, and our results apply to the infinite system as well. The results for different electronic densities can be understood in terms of universal scaling laws. (C) 2004 Elsevier B.V. All rights reserved.