No, how do we observe that there is no time and space before the "Bing Bang"? Or is it derived from the math in the thoery?
There are several models. But from my understanding there is not a "before the Big Bang" in most of them. We do not know this yet, but the math indicates it. More work in physics still needs to be done. The James Webb Telescope may answer some of these problems.
Here is the problem with the phrase "before the Big Bang", it may be nonsensical. The analogy often given is that of being "South of the South Pole". The phrase is nonsensical. Time and space may have begun with the Big Bang. Please note at this point there is no absolute clear model. But there are models that are better accepted than others. Scientists are keeping an open mind while trying to solve the problems.
The problem in this thread is that too many people are thinking using Newtonian Physics. Now that works fine on a medium scale. It is accurate enough to get us to the Moon and back. It is accurate enough for 99% of the situations that one runs into. But it fails when physics gets very small, or very large or very fast, or the very accurate. The last one is the most common one that you will run into. Newtonian Physics is "wrong" when it comes to GPS. Errors accumulate if one uses it. GPS systems have to account for both General and Special Relativity.
Let's get back to expansion of the universe. Thinking that the universe would have to expand into something is using Newtonian Physics and that physics does not apply at all when it comes to expansion. Relativity does not need a something else for the universe to expand into.