“Therefore even though we can’t directly observe it we know it is logical that it should exist...”
That’s called a non sequitur.
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Have you ever entered an elevator and gone to the top of a tall building? Do you ever give any thought to the foundation of the building even though you can’t directly observe it? It’s logical that the foundation exists simply by the fact of your presence at the top of the building.
I don’t need to directly observe everything to know that it’s there. And while that may not constitute a scientific proof to you I’ve yet to encounter the tall building that didn’t have a foundation.
Likewise the existence of more than just four dimensions to me is equally rational and obvious.
That metaphor doesn’t support your contention anymore than the previous argument did.
I mean, I could apply your metaphor to anything unobservable, for example:
“Since I can assume a tall building has a deep foundation without directly observing it, I can also assume that God exists without observing Him.”
“Since I can assume a tall building has a deep foundation without directly observing it, I can also assume that there is a pot of gold at the end of the rainbow without observing it.”
et cetera...
The problem lies in the fact that, unlike higher dimensions, God, or pots of gold at the end of the rainbow, with buildings, we actually design them. We discovered the principles required for their design through experimentation, and so we have those principles to rely on when we make our assumptions. Thus our assumptions are quite solid, being based on known and tested principles. Comparing assumptions based on known and tested principles to assumptions based only on theoretical constructs is not a proper comparison.