Salaamun Alaykum

As you have quite correctly pointed out, the primary emphasize of the Qur'anic cosmology is to identify the creative agent behind it, not the particulars of creation itself. As such, very few specifics are mentioned about the process itself. (Although a few details have been mentioned, these are not sufficient to provide an exhaustive creation story.)

The big bang theory is a scientific hypothesis that was originally theorized by a Catholic priest who also was a scientist. Before this theory, many scientist subscribed to the view that the universe was eternal. I point this out to demonstrate that science is constantly evolving.

The big bang theory is indeed supported by many observations. If you find that the evidence/observations support the hypothesis, then you do not need permission from someone else to accept it as an explanation for how our universe came about. In the same manner, if someone is not convinced by the evidence, then no matter what any authority says, they will not accept it.

From the Quranic perspective, what is important is that you recognize God as the creator of everything.

I would, however, suggest phrasing this differently. If the evidence convinces you, I would suggest saying that "I accept the big bang theory as the most convincing explanation of the evidence".

And God knows best

In need of your prayers

Hassanain