It’s a true statement: the graph of our history is infinitely long.
A graph of our history is not our history. Saying that our history is infinitely long because in some coordinates its beginning may have t=-\infty is like saying the North Pole is infinitely far away because it is drawn there on Mercator projection maps. Anyway, it’s not the graph of our history; there are many graphs and only some of them are infinitely long.
Coordinate time has no physical meaning,
I can’t agree with that statement.
It would be actually helpful if you also said why.
and it’s possible to choose the coordinates in such a way to have the time difference finite.
That much is true, but it fails to reveal explicably the nature of why the question, “What happened before the Big Bang?” as being as meaningless as “What’s further North than the North Pole?”
We aren’t discussing the question “what happened before the Big Bang”, but rather “how long ago the Big Bang happened”.
A graph of our history is not our history. Saying that our history is infinitely long because in some coordinates its beginning may have t=-\infty is like saying the North Pole is infinitely far away because it is drawn there on Mercator projection maps. Anyway, it’s not the graph of our history; there are many graphs and only some of them are infinitely long.
It would be actually helpful if you also said why.
We aren’t discussing the question “what happened before the Big Bang”, but rather “how long ago the Big Bang happened”.