  We present the first-ever cosmological constraints from a simulation-based
inference (SBI) analysis of galaxy clustering from the new ${\rm S{\scriptsize
IM}BIG}$ forward modeling framework. ${\rm S{\scriptsize IM}BIG}$ leverages the
predictive power of high-fidelity simulations and provides an inference
framework that can extract cosmological information on small non-linear scales,
inaccessible with standard analyses. In this work, we apply ${\rm S{\scriptsize
IM}BIG}$ to the BOSS CMASS galaxy sample and analyze the power spectrum,
$P_\ell(k)$, to $k_{\rm max}=0.5\,h/{\rm Mpc}$. We construct 20,000 simulated
galaxy samples using our forward model, which is based on high-resolution ${\rm
Q{\scriptsize UIJOTE}}$ $N$-body simulations and includes detailed survey
realism for a more complete treatment of observational systematics. We then
conduct SBI by training normalizing flows using the simulated samples and infer
the posterior distribution of $\Lambda$CDM cosmological parameters: $\Omega_m,
\Omega_b, h, n_s, \sigma_8$. We derive significant constraints on $\Omega_m$
and $\sigma_8$, which are consistent with previous works. Our constraints on
$\sigma_8$ are $27\%$ more precise than standard analyses. This improvement is
equivalent to the statistical gain expected from analyzing a galaxy sample that
is $\sim60\%$ larger than CMASS with standard methods. It results from
additional cosmological information on non-linear scales beyond the limit of
current analytic models, $k > 0.25\,h/{\rm Mpc}$. While we focus on $P_\ell$ in
this work for validation and comparison to the literature, ${\rm S{\scriptsize
IM}BIG}$ provides a framework for analyzing galaxy clustering using any summary
statistic. We expect further improvements on cosmological constraints from
subsequent ${\rm S{\scriptsize IM}BIG}$ analyses of summary statistics beyond
$P_\ell$.
