@TinoPup Apologies for the late response and if I am beating a dead horse, but I was browsing random galleries and just came across this.
This is definitely a Common Snapping Turtle (Chelydra serpentina). While they do have smoother shells than Alligator snappers, they are not always or entirely smooth. They do actually have ridging in hatchlings and young individuals that smooth out as they grow to adulthood. This individual does not look big enough to be a full adult, so I would still expect ridging to be present (but the size is hard to determine for sure).
Even without the shell, the head is a dead giveaway that this is Chelydra serpentina; less bulky head, more "prominent" eyes, smaller and less prominent beak, and they lack the fleshy "eyelashes" that Macrochelys temminckii has.
Also, Bays Mountain is outside the range of Macrochelys temminckii, but within the range of Chelydra serpentina, though I am not sure how much that matters. I assume this place mainly exhibits natives?
@Astrotom3000 Thank you for the detailed response! Yes this is a juvenile, maybe a foot long tip of nose to tip of tail. I'll have to try and remember those head details.
They exhibit natives but not just local natives. They have several California kingsnakes and a Sinaloan milk snake, for example. I assume those were donated pets.