Is there any realistic way we can see or travel to alternate universes and dimensions?

We’re bound to our dimensions, and so our universe. For all we know, we’re messing around in others’ universe without knowing it; just as we may be influenced by others in another universe without knowing it. We can tell a lot about our physical universe, but most is quite mysterious. So, we may be traveling/seeing (in part or whole, or in-and-out, or upside-down, but likely unbeknownst) in another universe right now; it’s just our understanding and physicality are confounded.

If we’re able to do what you ask, it may require us to be in a bizarre state, such as near the speed of light or in a black hole. Realistically, we cannot achieve these states as far as we can do or know now. Mathematics, astronomy, and engineering cannot accommodate this. We may never know or do this great deed; but that’s why we study so deep.