Kagome lattice decorated with S = 1/2 spins is one of the most discussed ways to realize a quantum spin liquid. However, all previous material realizations of this model have suffered from additional complications, ranging from additional interactions to impurity effects. Recently, a new quantum kagome system has been identified in the form of averievite Cu5-xZnxV2O10(CsCl), featuring a unique double-layer spacing between the kagome planes. Using muon spin spectroscopy we show that only a complete substitution (i.e., x = 2) of interplanar copper ions leads to a quantum-disordered ground state. In contrast, the parent compound (x = 0) exhibits long-range magnetic order, with a phase transition around 24 K. Experiments performed on the partially substituted material (x = 1) show that the transformation proceeds through an intermediate disordered, partially frozen ground state, unaffected by pressures up to 23 kbar. Our study provides a microscopic view of the magnetism of the decoupling of the kagome layers and establishes the averievite as a new material platform for the experimental study of the fully-decoupled kagome layers.