Applications for citizenship are processed by the notary so they will have the latest information.
From memory, an ADULT, or an emancipated minor who has been resident for more than 5 years can apply. I assume your son isn't emancipated so that route wouldn't apply.
Children of foreign parents can acquire citizenship subject to conditions, one of which is the child must have been born in Portugal to parents who have been legally resident for 5 years. As your son was 3 when you moved here that route wouldn't apply.
There was a proposal a couple of years ago for all children of foreign parents legally resident in Portugal to have the right of citizenship if they had attended school in Portugal but it wasn't approved by the president and was watered down to what I wrote in the previous paragraph.
But that's just my recollections of the process, the notary will be able to confirm.