My premise was that the universe was universal, i.e. there is no other universe. Again, I'm not saying that this is the case, or that there is any reason to believe that it is so, but I don't see a good reason why there would be more than one universe. (Note that all of this depends a bit on the definition of a universe -- for the sake of argument, I'm assuming our universe to be a system closed under physical interactions. Happy to argue about other universes, but perhaps it's best to save that for another time.)

If you are trying to prove the existence of this universe by requiring the existence of another universe, then it's turtles all the way down.

How do you define "existing" of a pattern? Does it exist inside a physical thing? If so, then how does that physical container come into existence? And if it exists only conceptually, then how is it possible for concepts to exist? In the universe that I know, concepts only exist in the minds of human beings, and perhaps in some other animals. To me, it seems rather unlikely (and a bit anthropocentric or egocentric) that concepts are something truly universal.

For me, it helped to meditate a lot on what it'd be like to be a rock. The rock does not have memory, no sensory input, and therefore most likely no concept of time, space, logic, nor mathematics. It makes you wonder whether the rock exists at all. In any case, it probably doesn't care as much about it as we humans do. There might be a hint there.