The scenario in which kids skip the babbling and single-word development phases and go straight from non-verbal to speaking in fully-formed sentences around 30-36 months seems to be quite common among aspies. My mother told me that I didn't babble or cry much and learned 5 words (yes, no, hi, bye, mine) by my first birthday. I then didn't say anything at all for almost two more years. Then one day I just opened my mouth and began speaking in coherent and fully-formed sentences and had a substantial vocabulary.
As far as diagnostic criteria goes, there is a misconception that if you didn't speak by age 3 then that makes you autistic. The criteria is actually based on communication skills, not speech. If a child doesn't speak by age 3 but is otherwise be able to communicate using gestures, pointing and shared gaze then they would not be considered autistic in the classic sense.
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What would Flying Spaghetti Monster do?