At least not with current technology.
Our universe is massive and unfortunately there will always be parts of it that we will probably never, ever be able to see. Not just because of its enormous size, but because it is expanding faster and faster every second.
According to a video posted by Fraser Cain titled What Will We Never See?, when we look out to distant stars and galaxies, we are actually looking backwards in time, and the edge of what we can see is known as the Cosmic Microwave Background Radiation. This is the point, about 300,000 years after the Big Bang, that everything had cooled enough that light could finally escape and travel through the universe. What happened before 300,000 passed is still a mystery because we just can’t see it.
How about the very distant future? Assuming humans are still around to observe the universe, there unfortunately will be a lot less to see. Since the expansion of the universe is accelerating, galaxies are moving further and further away from each other — and us. Eventually, they will be moving faster than the speed of light, and when this happens we won’t be able to see any distant galaxies at all. It will just look empty.
Now, let’s talk about the ever-so-popular black holes and their event horizons. We can’t look inside the event horizon because gravity is so strong that not even light can escape. So we can’t see what absorbs all of the light. Astronomers are still unsure if black holes stop shrinking in size over time or if they shrink forever — getting smaller and smaller into infinity.
However, there may be a trick to seeing inside some of these hidden places — using gravity. When black holes form, or when massive objects crash into each other, they generate distortions in spacetime called gravitational waves.
Just like gravity, these waves propagate across the universe. If we could detect them, we could use these gravitational waves to “see” beyond the event horizon of a black hole, or even beyond the Cosmic Microwave Background Radiation.
The only problem with this idea is that gravitational waves are very faint, and we so far have not been able to detect any. This is probably because current technology is not yet sensitive enough — but we are getting close.
In the meantime, I think there is enough in our observable universe we are still trying to understand to keep us busy.