What exists beyond our Universe?
You assume that (a) your Universe is singular, and (b) therefore, there is something in a singular way “beyond” it.
Your Universe is part of a multiverse of created events that exist simultaneously in various time frames. They overlap in very interesting ways, and every so often they collide, bringing a “big bang” type of event that will actually create another 4D Universe. So the question is answered first in this way: What is beyond your Universe is what coexists with it, interdimensionally, in the same space.
It's a far more complex thing than you think, since there's a lot more of it than you can see in 4D. Still, you ask a good 4D question about what is actually beyond the limits of your known 4D Universe. The second answer is something you won't comprehend: What's beyond it? It's an infinite space seeming like nothingness, ready for even more Universes. Yours folds and folds, so it's really not quite as large as you think, but the space around it goes on forever... no limitation... no ending... just like your own divinity. Your Human brain detests things that don't have containment and won't fit in a box. This doesn't have containment in your perspective, but there's always something present in all of it, even if it appears to go on “forever.”