If I could place myself beyond the expanding universe. Would I then perceive something or would I simply no longer exist?

Answer

“If I didn’t exist, I wouldn’t exist.” What I mean by this is that there is not much point in asking what would be the result of something that is impossible. And what is impossible here is to teleport yourself at a speed greater than the speed of light.

The space and time we know are connected to our universe. If you write ‘outside’, you extrapolate the concept of space beyond where it is valid. By the way, you implicitly acknowledge this by putting ‘place’ in quotation marks. In a sense, the answer to your question is indeed what you feel: our existence and our laws of nature are not conceivable outside the context of our universe.