The straightforward answer is that you are born the heir of someone who is already the monarch.
A better answer for the UK in line with your point about religious recognition is that you are anointed monarch. There is a coronation ceremony where the heir is anointed with holy oil (chrism) by the Archbishop of Canterbury. After that, they stop being an ordinary person and become monarch.
You can see part of the coronation of Elizabeth II (and hear the incredible Zadok the Priest coronation anthem by Handel) here [0], although not the anointing itself, because it happens under a canopy and has never been filmed.
Actually, not true. What you're referring to is known as primogeniture succession, but there were also elective monarchies and tanistry, and probably more that I don't know about. Sometimes succession was limited to the immediate family, sometimes a 'bloodline', sometimes any eligible nobles.
For example that article mentions the Kingdom of Italy was briefly had this as the succession law:
The Kingdom of Italy was designated a secundogeniture for the second surviving son of Napoleon I Bonaparte but, failing such, provided for the emperor's stepson, Eugène de Beauharnais, to succeed, even though the latter had no blood relationship to the House of Bonaparte
Actually, it is true but not exhaustive. Nor was it intended to be. I was addressing the context of monarchy in the UK, as the rest of the comment makes clear.
The GP was asking in general, so your straightforward answer is explicitly wrong and must be read in that context, whether the UK's one happen to evolve into one is a bit irrelevant. Then again, even in 'recent' history, William of Orange was invited to take the English crown without primogeniture.
A better answer for the UK in line with your point about religious recognition is that you are anointed monarch. There is a coronation ceremony where the heir is anointed with holy oil (chrism) by the Archbishop of Canterbury. After that, they stop being an ordinary person and become monarch.
You can see part of the coronation of Elizabeth II (and hear the incredible Zadok the Priest coronation anthem by Handel) here [0], although not the anointing itself, because it happens under a canopy and has never been filmed.
[0]: https://www.youtube.com/watch?v=X-QvwFWTB5c