We don’t, fundamentally. All we can do is construct models and see if they match our observations. How do we know the world exists beyond our sensation of it? That could be an illusion too.
The base assumption that we work on is that the universe is the same here as it is there. Same rules, same interactions. We work out what we should be able to see and then go looking for it, so far that has worked.
As an example, we can look at some hydrogen in a lab and see what kinds of light it absorbs, we can then look at the sun and see if it is absorbing the same light, we can then look at another star and see that it two is absorbing the same light. So we can be confident that the hydrogen in our lab is like the hydrogen in the sun, and that the distant star is made of the same stuff as our sun. We can do wlthis with each element. We can look at the motion of planets around the sun, and we can look at the motion of stars around the center of the galaxy and see that they follow the same patterns.
It’s like trying to work out what is going on in the next room by listening, you can get a good idea, but it could be an empty room with a radio.