There's nothing wrong with the sentence. :)
"If you were to write out your brain's potential..." - How? In what way? Creatively or technically? Or another way?
"...as expressed by the number of possible neural connections it could make..." - In this way. So, we have a quantitative measure.
Removing "as" would be a mistake. The sentence would become broken. Adding "it was" would also be a mistake. The useful phrase here is "as expressed by (this)", to mean "shown in this way".