The quantum metric, the real part of a quantum geometric tensor, plays an important role in fundamental transport and optical responses of quantum materials. While net quantum metric effects are typically realized by breaking both time-reversal ($\mathcal{T}$) and inversion ($\mathcal{P}$) symmetries, valley-contrast mechanisms enable the probing of quantum geometry in centrosymmetric, nonmagnetic systems, revealing physical signatures beyond Berry curvature. Here, we design a four-layer ${\mathrm{MoS}}_2$ platform that combines sliding antiferroelectric order with strain-induced $C_{3z}$ breaking to realize a quantum metric driven nonlinear valley Hall effect (NVHE) under preserved $\mathcal{P}$ and $\mathcal{T}$ symmetries. Reversible interlayer sliding ($\mathrm{ABBA}\leftrightarrow \mathrm{BAAB}$) provides nonvolatile electrical control of the valley response. First-principles calculations reveal an outer-layer-dominated NVHE with tunable sign and magnitude. This symmetry-preserving, sliding-tunable strategy activates hidden quantum geometric phenomena in realistic two-dimensional materials and opens a clean pathway for tunable valleytronics and quantum information devices.

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• Antiferroelectricity
• Electrical properties
• Hall effect
• Valleytronics
• Density functional calculations