We define and apply a method to study the non-vanishing of [Formula: see text]-adic cyclotomic multiple zeta values. We prove the non-vanishing of certain cyclotomic multiple harmonic sums, and, via a formula proved in another paper, which expresses certain cyclotomic multiple harmonic sums as infinite sums of products of [Formula: see text]-adic cyclotomic multiple zeta values, this implies the non-vanishing of certain [Formula: see text]-adic cyclotomic multiple zeta values.