How does a person know what is true concerning cosmology and other areas of astronomy?
There are many methods of determining the relative probability of scientific theories. the first one is direct observation. For example, many theories about the nature of planets that were originally based on indirect evidence have now been tested by close flybys of those planets or actual landings on them. Observations of distant galaxies are interpreted according to an assumption of the uniformity of natural laws. For example, if a certain element generates a certain pattern of absorption lines in laboratories on earth, and we see that same pattern in the spectrum of a star, we know that element is present. If we see those lines red-shifted, we know the distant object containing that element is moving away from us. If in every direction we look, objects are red-shifted, we can calculate the rate of expansion of the universe and extrapolate back to discover its age and origin.