Just to say you've got some good answers here, and it's mainly about lack of complete certainty but we make reasonable assumptions about what is likely to be going on. It's not so very different from everyday life. I don't know for sure what my cat is doing right now (it's not in the room with me at the moment) but I'm pretty sure it is not peeling a banana or riding on a bike. Very likely it is asleep.
However, when it comes to the universe at large there is an interesting observation to make, which is that we receive light from only a tiny fraction of the whole. We gather information arriving at Earth from our past light cone, and that's it: a tiny sliver from the whole history of the cosmos. You can often find statements referring to 'the observable universe' and then the speaker goes on to describe things way way out of our past light cone, sometimes without realising that they are doing so. It's a reasonable hypothesis that a galaxy we can see at a large red shift has, since then, evolved in a similar way to other galaxies of similar make up. But such a hypothesis is only good to the extent that there is uniformity as opposed to richness and variety in the universe. In practice the universe combines both. It is not a desert, but neither is it a jungle.