The initial-state geometry in relativistic heavy-ion collisions provides a novel probe to nuclear cluster structure. For ^{20}Ne, a novel approach is proposed to distinguish between the cluster configurations (5α versus α+^{16}O) in order to gain insight into nuclear structure transitions governed by many-body quantum correlations. Through analytical calculations with the microscopic Brink model and event-by-event simulations using the hydrodynamic framework, we establish the normalized symmetric cumulant NSC(3, 2) and the Pearson coefficient ρ_{2}(v_{2}^{2},δ[p_{T}]) as quantitative discriminators to reveal enhanced cluster degrees of freedom in the ground state of ^{20}Ne. The ultracentral Ne+Ne collisions at the LHC can experimentally identify these two competing configurations via these flow correlation observables, opening a new paradigm for probing clustering in light nuclei.