The advancement of earthquake early warning systems (EEWS) plays a pivotal role in reducing the detrimental impacts of seismic events on human lives and infrastructure. This paper introduces a novel method for synthesizing seismic digital waveforms tailored specifically for EEWS applications. The method leverages Green's functions, which effectively characterize the Earth's response to a point source. By utilizing these functions, we simulated the propagation of seismic waves originating from diverse earthquake sources and tracked their movement to a designated receiver location. To evaluate the effectiveness of this approach, we conducted a thorough validation by comparing the synthetic seismic waveforms produced by the proposed method with real seismic waveforms recorded from historical earthquakes. The results demonstrate that the synthetic waveforms align closely with the real data in terms of amplitude, frequency content, and arrival times. This accuracy underscores the potential of the proposed method to significantly enhance the precision of seismic waveform simulation, thereby strengthening the foundation of EEWS.