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The 3D distribution of galaxies encodes detailed cosmological information onthe expansion and growth history of the Universe. We present the firstcosmological constraints that exploit non-Gaussian cosmological information onnon-linear scales from galaxy clustering, inaccessible with current standardanalyses. We analyze a subset of the BOSS galaxy survey using ${\rmS{\scriptsize IM}BIG}$, a new framework for cosmological inference thatleverages high-fidelity simulations and deep generative models. We use twoclustering statistics beyond the standard power spectrum: the bispectrum and aconvolutional neural network based summary of the galaxy field. We inferconstraints on $\Lambda$CDM parameters, $\Omega_b$, $h$, $n_s$, $\Omega_m$, and$\sigma_8$, that are 1.6, 1.5, 1.7, 1.2, and 2.3$\times$ tighter than powerspectrum analyses. With this increased precision, we derive constraints on theHubble constant, $H_0$, and $S_8 = \sigma_8 \sqrt{\Omega_m/0.3}$ that arecompetitive with other cosmological probes, even with a sample that only spans10% of the full BOSS volume. Our $H_0$ constraints, imposing the Big BangNucleosynthesis prior on the baryon density, are consistent with the early timeconstraints from the cosmic microwave background (CMB). Meanwhile, our $S_8$constraints are consistent with weak lensing experiments and similarly liebelow CMB constraints. Lastly, we present forecasts to show that future workextending ${\rm S{\scriptsize IM}BIG}$ to upcoming spectroscopic galaxy surveys(DESI, PFS, Euclid) will produce leading $H_0$ and $S_8$ constraints thatbridge the gap between early and late time measurements and shed light oncurrent cosmic tensions.

${\rm S{\scriptsize IM}BIG}$: The First Cosmological Constraints from Non-Gaussian and Non-Linear Galaxy Clustering