Coalescing ballistic annihilation is an interacting particle system intended to model features of certain chemical reactions. Particles are placed with independent and identically distributed spacings on the real line and begin moving with velocities sampled from $-1,0,$ and $1$. Collisions result in either coalescence or mutual annihilation. For a variety of symmetric coalescing rules, we prove that the index of the first particle to arrive at the origin does not depend on the law for spacings between particles.