I read this book, "Measuring The Cosmos", a few years ago, and it talks about the various ways we use to establish distances to such far objects. The book describes how we grew our "measuring tape" so to speak. We started with learning accurate distances to things closer, the distance from the Sun to Earth, an AU, being one of those. That's useful for local solar system distances, but the numbers become too big for human consumption when measuring further objects. Light years became the next rung on the ladder. Parsecs next, etc.

Now, we use certain types of stars like pulsars that have known brightness for the particular frequencies. Once we find a new pulsar that matches, we can compare how bright it is to others of the same type. If it is brighter, it is closer. If it is dimmer, it is further away. I'm way way oversimplifying it, but hopefully it gets the concept across.

https://www.amazon.com/Measuring-Cosmos-Scientists-Discovere...