When a bank borrow you money they don't actually take it from somewhere they fundamentally can create it because of quantitative easing pushed by central banks.
The digital monetary system today is a far cry from the gold based system and the ability to use money as if they are income are very real. Money is more a concept today.
They can't do it without the Central Bank and it's the same mechanism as allows for QE. It's only possible in a FIAT based system.
When banks do it it's called fractional reserve banking but the mechanism is fundamentally the same, the ability to "create money".
There's no mandate that bank notes need to be issued by a central bank. See the article: https://en.wikipedia.org/wiki/Banknote
So yes it requires a central bank as it's through them the recognition happens. Philosophically all money requires is trust no matter what not even a legal entity as long as people trust it, but practically to claim that central banks aren't needed for FRB is wrong to the best of my knowledge.