GR is GR. GR is not the big bang. It's GR. Saying that GR allows a big bang is like saying that our moon allows black holes to exist.
Lambda-CDM model provides a reasonably good account of the following properties of the cosmos:
-background radiation
-distribution of galaxies
-abundance of hydrogen and other
-the accelerating expansion of the universe
None of that is evidence of a big bang. The background radiation is cold space. Cold space does not prove a hot big bang. Space has always been cold.
The distribution of galaxies just means that galaxies are distributed. It does not prove a single big bang.
The abundance of hydrogen and other elements just means that hydrogen is abundant. Hydrogen does not mean there was a big bang. It just means that there is more hydrogen than other elements.
The accelerating expansion of the universe? This is evidence against a big bang. Scientists thought the universe would show a slowing down of the expansion because of gravity but what they see is it increasing expansion rate. That means that something else is at work. Big bangs don't increase in speed 13.8 billion years after the event.