It's Official: We Were WRONG About the Big Bang

This was a very good afternoon at answering very complex astronomical and cosmological questions however even though I have a master's degree in physics I'm still a little confused at some of the answers you give in the video. Firstly, I get that the Big Bang is a very bad description of the early universe in that there was no bang, no explosion, but expansion.

Secondly, having thought about this quite a lot I understand that the fabric of space-time is expanding, so when it is asked where in space is where the so called Big Bang and saying it is everywhere, it's just space-time has stretched like a balloon being inflated and that it's just that because of inflation everything that was close together at the time the expansion began is now very far apart in some cases.

Thirdly, and probably more related to what is discussed is the video, how do we now know that the universe is expanding into something? How can we ever know this? As time increases, as the fabric of the universe is expanding faster than the speed of light objects that are one within the visible universe are now so far away that the light from them can never get to the Earth, and if there is matter even further away that we could never see before then that's never, ever been able to be observed by humans. Isn't your answer to this pure speculation and since it can't be treated experimentally not even scientific, but purely philosophical?

If anyone has any thoughts on the points I raised please let me know, I'd love to hear some people's thoughts.