The propagation of spin waves in magnetically ordered systems has emerged as a potential means to shuttle quantum information over large distances. Conventionally, the arrival time of a spin wavepacket at a distance, d, is assumed to be determined by its group velocity, v_g. Here, we report time-resolved optical measurements of wavepacket propagation in the Kagome ferromagnet Fe₃Sn₂ that demonstrate the arrival of spin information at times significantly less than d/v_g. We show that this spin wave "precursor" originates from the interaction of light with the unusual spectrum of magnetostatic modes in Fe₃Sn₂. Related effects may have far-reaching consequences toward realizing long-range, ultrafast spin wave transport in both ferromagnetic and antiferromagnetic systems.