We present the first post-cosmic-microwave-background early-Universe observational constraints on σ 8 , Ω m , mean galaxy star-forming efficiency and galaxy UV magnitude scatter at redshifts z = 4 − 10. We perform a simultaneous 11-parameter cosmology and star-formation physics fit using the new code GalaxyMC, with redshift z > 4 galaxy UV luminosity and correlation function data. Consistent with previous studies, we find evidence for redshift-independent star formation physics, regulated by halo assembly. For a flat ΛCDM universe with a low-redshift Hubble constant and a Type Ia supernovae Ω m prior, we constrain σ 8 = 0.81 ± 0.03, and a mean star-forming efficiency peaking at log 10 SFE = −[(0.09±0.20)+(0.58±0.29)×log 10 (1+z)] for halo mass log 10 M p /h −1 M = 11.48±0.09. The suppression of star formation due to feedback is given by a double power law in halo mass with indices α = 0.56 ± 0.08, β = −1.03 ± 0.07. The scatter in galaxy UV magnitude for fixed halo mass is σ M = 0.56 ± 0.08. Without a prior on Ω m we obtain σ 8 = 0.78 ± 0.06, Ω m = 0.33 ± 0.07 and at most 1σ differences in all other parameter values. Our best-fit galaxy luminosity functions yield a reionization optical depth τ ≈ 0.048, consistent with the Planck 2018 value.