Is this real-time, cross-universe communication system physically viable?

Suppose that there's a button at the other end of the universe, and a 'stick' that goes all the way there.

If I push the stick, will the button get pushed instantly, or there is some latency that I am missing?

(Suppose that the stick is made from whatever strong enough material that can stand whatever physical or practical constraints over there.)

I want to use this mechanism to build a real-time communication system that spans multi-light-years areas. So is this a good idea?

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Is this real-time, cross-universe communication system physically viable?

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