Because we can see the distribution from the CMB, 380,000 years after the big bang. It's almost perfectly homogenous and isotropic. The images you see of the CMB are amplified a lot, the deviations are on the order of 10^-5 or something.
This in turn puts constraints on the primordial quantum fluctuations that were inflated during the inflation phase, and backtracking through simulations it puts constraints on the entire dark matter and matter history from now back to age 380,000 years.
This in turn puts constraints on the primordial quantum fluctuations that were inflated during the inflation phase, and backtracking through simulations it puts constraints on the entire dark matter and matter history from now back to age 380,000 years.