I still don’t get it - why couldn’t it be that everything outside our solar system is antimatter, and we live on the only island of matter in the universe? Just because we haven’t found an easy way of producing antimatter doesn’t mean there can’t be a mechanism for the universe to do so. Since matter and antimatter are visually indistinguishable (right?), how do we know whether the galaxies and stars we observe outside our own are matter?
For galaxies, eburacum45’s point is the best evidence: there are lots of examples of colliding galaxies. Now, when galaxies collide the stars in them typically don’t crash into each other. They’re a bit too spread out for that to happen. But there’s more to a galaxy than just stars and they also contain lots of clouds of gas and dust. During the collisions gas and dust from the two galaxies does crash into each other. As these things go, that’s pretty violent and so such collisions generate lots of radio waves and X-rays from where the gas and dust is impacting. Now, if the different galaxies were matter and antimatter respectively, it’d be obvious from such impacts of gas and dust during the collisions. For a start, the events would be much, much more violent than they already are. Furthermore, the characteristics of the radiation given off in the collisions would obviously be different from what’s seen. So we can be pretty certain that other galaxies contain gas and dust that’s predominately matter, like in our own.
As for stars, in any galaxy where the gas and dust is matter, we can be pretty sure that all the stars are as well. For a start, it’s from such stuff that the stars in the galaxy came from in the first place. There’s also plenty of interaction observed between stars and such stuff. Stars run into gas clouds or they blow up and spew shockwaves of what used to be part of themselves into the clouds. In none of these processes do we see any evidence of matter/antimatter annihilation.
Finally, while it’s not empirical evidence that the universe is predominately made up of matter, that it is is something that can be explained. In current models of the very, very early universe, things originally started off symmetric. There was equal amount of matter and antimatter. However, processes are observed in high-energy physics experiments which show an imbalance between the two. On average they slightly favour matter over antimatter. In the models, these processes mean that some of the antimatter became matter during the very early stages of the Big Bang. The rest of the antimatter then annihilated with some of (most of, actually) the matter then about, leaving the current situation. That we mainly see matter in today’s universe thus isn’t terribly mysterious. As cosmology goes.
Even in the vast intergalactic voids, there are occasional hydrogen atoms floating around. All of the hydrogen atoms in our vicinity are the type with positive protons and negative electrons-- What we refer to as “matter”. If, somewhere, the dominant form were antimatter, then there would be regions where the matter and antimatter came together. And even at the extraorinarily low densities of deep space, they’d occasionally collide and produce some very distinctive gamma rays. We would be able to see these gamma rays if they existed, but we don’t. Conclusion: There are no boundaries between matter and antimatter regions, and since our local neighborhood is matter, the entire visible Universe must be matter. It is still possible, though, that there are regions of antimatter, so long as the nearest is more than 13.7 billion lightyears away.