This is incorrect. Are you familiar with the inverse-square law? In 3-dimensional Euclidean space, the rate at which any force decays over a distance is inversely proportional to the square of the distance. This generalizes to n dimensions; but instead of the drop off rate being inversely proportional to the square of the distance, it becomes inversely proportional to the n - 1th power of the distance.
Suppose our universe is a 3-dimensional embedding of a n-dimensional manifold. Every local force we could empirically test would adhere to the inverse-square law, i.e. have drop off over distance k of ~ 1/(k^2). But theoretically speaking we could empirically test the dimensions of the manifold we reside in by identifying which power of distance is proportional to the drop off rate of extremely small forces where the compactified dimension can be detected.
For practical purposes this would require us to increase the precision with which we can empirically test (and reason about) forces at the subatomic level.
That's not evidence FOR the superverse, just like we can inherently not rule out the idea of the https://en.wikipedia.org/wiki/Evil_demon deceiving our every perception.
At best, this is untestable philosophy that's fun to debate over drinks. At worst, it's a tedious discussion about the semantics of existence and time.
Don't get me wrong! We could discover interesting things about our universe looking for holes, but there's no indication this problem is tractable.
Imagine if we came up with a super-universe theory that said that the super-universe could only spawn sub-universes which followed conservation of energy plus several other laws no one had ever thought to test before (and weren't implied by any other theories), and as we started testing for those other laws, every single one we tested turned out to hold in our universe.
(If that happened, it would be reasonable to look for simpler theories that also predicted those other laws too, but it's possible that the super-universe theory would turn out to be the simplest possible theory that fits. Theories should be judged by the complexity of their rules, not by the number or complexity of things they predict; a simple theory that implies a large ensemble of universes can be better than a more complex theory that implies only our world or what we can see is real.)
This is also meaningless, scientifically: there is nothing you can measure which is outside the universe. Things like a holographic universe are inherently untestable. I hope we continue looking for testable things, but this speculative path rapidly leads away from science and physics and into "linguistic tricks to confuse humans". It's not even philosophy at that point, it's just arguing over semantics.