Again, learning notation is part of the process of learning math. No one is gatekeeping anything, at no point you need to do an exam or magically be aware of notation that you never saw. Every book and every class will define new notation at the beginning, in most cases they will do so even when there’s no new notation. I am not sure what your argument is.
That’s a very good gate to keep. Some things are just meant to be gatekept so that the cranks and dilettantes that wastes everyone’s time can stay far outside.
"In order to enter this gate you must know what this symbol means."
"I am unfamiliar with that symbol."
"Well, I expect you to learn what it means before I allow you to enter this gate. Now go away."