What evidence do we have that our universe created space/time at the Big Bang?

At the time Albert Einstein was thinking the universe and everything was stationary and non-expanding, There was a man named Edwin Hubble who was a famous astronomer. When he was looking through a large telescope observing nearby galaxies and discovered they were moving away at a rapid rate. This is called Hubble's law, and if we trace everything back 13.7 billion years we find a point in space with all of the energy in the universe there.

At this point this point continuously became more dense and unstable and exploded into a silent explosion creating both space and time. So yes the big bang did create space and time but, theories (which make perfect logical sense to me) say there are infinite to the infinitieth power of universes similar to ours and maybe not containing every possibility in existence. So, the answer to your questions... Hubble's law, (red shift and blue shift which you can look up) and multiverse theory containing every possiblity.

Our space-time is a property of our universe, even if we were expanding into an already existing multi-verse, the big bang would have been the creation of OUR space-time.

the big bang created our space time

But it could have been created in an already existing multidimensional UNIVERSE

I use the term UNIVERSE to describe a universe of many dimensions (As many as you like), not our 3 dimensional universe

If you imagine say a 2D universe existing in a 3D UNIVERSE e.g a sheet of paper

then many sheets of paper could exist 1 above another in 3 dimensions - e.g like a book

(so each 2D universe would be independent of other 2D universes but all would co-exist in a 3D UNIVERSE e.g like a book with tissue paper between each sheet).

So the existence of "time" in a "sheet" of paper could exist independently of "time" in other "sheets" or of the "book" itself. And all of the 2D universes would co-exist, but would be completely separate from, and could NEVER "touch", each other (i.e "words" on 1 sheet could never transfer to another)

Our 3D universe could exist in a multidimensional universe just as with a "sheet" in a "book"

But there is no evidence of any of this or of what you say.

None, the Big Bang theory is only abut the expansion, not the "creation" or any kind of "beginning". This is a common but serious mis-conception.

None that I'm aware of, it's just a philosophical point that the start of the universe was the start of time.

?????The universe IS space-time, not something made by it - are you saying that the universe is a god who can create something from nothing? A most peculiar circular question

Read my web site, given below, for all your answers.

All of the astrophysicists on earth.