I've seen this structure on a Quora post
Had I been a Muslim man, I would've been able to have sex plenty, and society wouldn't know at all because I would've had no hymen, but as a Muslim woman, my sins were easier to track.
What does that "Had I + Past participle verb" mean?
This is the post I'm referring to:
Best Answer
This is equal to the unfulfulled conditional (conditional 3)
The only difference between the two structutes is :
In the first sentence there is an inversion of the verb had and if is omitted..
The sentence means I was not a muslim man ( but I was a muslim woman), so I was not able to have sex plenty
In the link you provided, The woman thinks that as a muslim woman she did not have the freedom of a muslim man. She was not able to do what she wanted to do as she was a muslim woman
You can use similar structures in your writing.
Had I been a professor, I would have taught English lessons
Had I been a doctor, I would have treated the patients