The standard quantum limit bounds the precision of measurements that can be achieved by ensembles of uncorrelated particles. Fundamentally, this limit arises from the non-commuting nature of quantum mechanics, leading to the presence of fluctuations often referred to as quantum projection noise. Quantum metrology relies on the use of non-classical states of many-body systems to enhance the precision of measurements beyond the standard quantum limit. To do so, one can reshape the quantum projection noise—a strategy known as squeezing. In the context of many-body spin systems, one typically uses all-to-all interactions (for example, the one-axis twisting model) between the constituents to generate the structured entanglement characteristic of spin squeezing. Here we explore the prediction, motivated by recent theoretical work, that short-range interactions—and in particular, the two-dimensional dipolar XY model—can also enable the realization of scalable spin squeezing. Working with a dipolar Rydberg quantum simulator of up to N = 100 atoms, we demonstrate that quench dynamics from a polarized initial state lead to spin squeezing that improves with increasing system size up to a maximum of −3.5 ± 0.3 dB (before correcting for detection errors, or roughly −5 ± 0.3 dB after correction). Finally, we present two independent refinements: first, using a multistep spin-squeezing protocol allows us to further enhance the squeezing by roughly 1 dB, and second, leveraging Floquet engineering to realize Heisenberg interactions, we demonstrate the ability to extend the lifetime of the squeezed state by freezing its dynamics.