The experimental detection of nonequilibrium quantum criticality remains a challenge, as traditional signatures like dynamical quantum phase transitions rely on hard-to-measure global properties. Here, we demonstrate that local connected correlation functions provide an alternative, practical means to directly probe the dynamics of magnetic order in a quenched Rydberg-atom array. Using a Magnus expansion formalism, we derive analytic expressions for these correlations that capture a smooth crossover from antiferromagnetic to ferromagnetic dominance. Our analytic results, which reveal the critical parameter relationship $U_c\left(\delta \right)$, are validated against exact numerical simulations and exhibit robustness to finite-size effects. By shifting the focus from global singularities to local correlations, our protocol establishes a direct and feasible path to observe the rich critical dynamics in scalable quantum simulators.

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• Dynamical phase transitions
• Quantum simulation
• Rydberg gases
• Rydberg atoms & molecules