Is cosmology an accurate field? I'm new here this is my first question. I'm an engineering student and I really like mathematics, I've recently watched a movie about Stephen Hawking (The Theory of Everything) In which he makes various discoveries about black holes. This made me curious about cosmology and the only thing I know about this subject is

Cosmology is a branch of astronomy concerned with the studies of the origin and evolution of the universe, from the Big Bang to today and on into the future

This made me question how accurate it is, since there is no way to see
Your question is based on a false premise:

there is no way to see

On the contrary, the distant universe is being observed to infer information about cosmology and observational cosmology is a field of active research. Like all scientists, cosmologists make hypotheses and test them by making observations. Luckily for cosmologists, light travels at a finite speed, so by looking at objects very far away, you see how they were a long time ago.
A better question might be &quot;How do cosmologists know what they do?&quot;.
Here are a couple examples of things that have been observed to gain insight on cosmology.

Measuring the redshift of galaxies shows that the universe is expanding. Observations of type Ia supernova even indicate that this expansion is accelerating.
Observing the cosmic microwave background disproved some hypotheses about the early universe.
Comparing the amount of stars and gas in galaxies to the speed at which they spin shows that something is amiss, so more observations are being made to try to figure out what is going on.

Now, of course, we have to make some assumptions to make this all work. For instance, cosmologists generally assume that the universe is homogeneous and isotropic at large scales.