In my experience, the Lisp enlightenment comes in stages, two big ones are 1) s-expression parsing you describe here, and 2) grokking "code is data".
WRT. s-expressions enlightenment, I vividly remember when it happened to me. Few months into learning Lisp, I bought a hardcover SICP and, for some reason, decided to do exercises in it on paper. Few exercises in, as I was writing Lisp code with a pen in hand, suddenly something clicked in my head - like my brain JIT-compiled a new processing module - and from then on, I no longer needed to mentally count or track the parens. I just knew how many and where they were, it dropped to semiconscious level. Ever since, I'm very comfortable with s-expressions; in fact, I prefer them as a notation to Algol/C-like code.