In this contribution we introduce an approach to analyze the formation of Brillouin precursor in a signal propagated through a dispersive multilayered medium formed by sea-water and sea-ice. We theoretically predict the evolution and formation of the Brillouin precursor for one classical pulse used: the rectangular one. The design of a ramp pulse based waveform is proposed as near-optimal signal in terms of an improved peak amplitude decay level offered after travelling the multilayer scenario. The analysis herein offered results of interest in underwater applications, such as sensing, natural resources detection or communications.