Quantum Monte Carlo (QMC) methods offer exact solutions for quantum many-body systems but face severe limitations in fermionic systems like atomic nuclei due to the sign problem. While sign-problem-free QMC algorithms exist and provide valuable insights across disciplines, they have been restricted to simple models with limited quantitative predictive power. Here we overcome this barrier by developing a novel lattice nuclear force that is rigorously sign-problem-free for even-even nuclei. This interaction achieves a standard deviation of $\sigma =2.932\mathrm{MeV}$ from experimental binding energies for 76 even-even nuclei ($N,Z\le 28$), matching state-of-the-art phenomenological mean-field models. Key innovations include the first sign-problem-free implementation of spin-orbit coupling for shell evolutions and an efficient QMC-optimized framework for global parameter fitting. Using this approach, we compute binding energies from ${}^4\mathrm{He}$ to ${}^{132}\mathrm{Sn}$ with unprecedented one-thousandth level numerical precision, reproduce symmetric nuclear matter saturation, and reveal novel spin-orbit-driven clustering in light nuclei. This Letter transforms sign-problem-free QMC simulation into a scalable and predictive nuclear structure tool, while establishing a high-fidelity, nonperturbative foundation for ab initio calculations of heavy nuclei.

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• Binding energy & masses
• Nuclear many-body theory
• Nuclear structure & decays
• Nucleon-nucleon interactions
• Metropolis algorithm
• Monte Carlo methods
• Quantum Monte Carlo