  Simulation-Based Inference of Galaxies (${\rm S{\scriptsize IM}BIG}$) is a
forward modeling framework for analyzing galaxy clustering using
simulation-based inference. In this work, we present the ${\rm S{\scriptsize
IM}BIG}$ forward model, which is designed to match the observed SDSS-III BOSS
CMASS galaxy sample. The forward model is based on high-resolution ${\rm
Q{\scriptsize UIJOTE}}$ $N$-body simulations and a flexible halo occupation
model. It includes full survey realism and models observational systematics
such as angular masking and fiber collisions. We present the "mock challenge"
for validating the accuracy of posteriors inferred from ${\rm S{\scriptsize
IM}BIG}$ using a suite of 1,500 test simulations constructed using forward
models with a different $N$-body simulation, halo finder, and halo occupation
prescription. As a demonstration of ${\rm S{\scriptsize IM}BIG}$, we analyze
the power spectrum multipoles out to $k_{\rm max} = 0.5\,h/{\rm Mpc}$ and infer
the posterior of $\Lambda$CDM cosmological and halo occupation parameters.
Based on the mock challenge, we find that our constraints on $\Omega_m$ and
$\sigma_8$ are unbiased, but conservative. Hence, the mock challenge
demonstrates that ${\rm S{\scriptsize IM}BIG}$ provides a robust framework for
inferring cosmological parameters from galaxy clustering on non-linear scales
and a complete framework for handling observational systematics. In subsequent
work, we will use ${\rm S{\scriptsize IM}BIG}$ to analyze summary statistics
beyond the power spectrum including the bispectrum, marked power spectrum, skew
spectrum, wavelet statistics, and field-level statistics.
