Olive Smith (Pitt) - Did this Olive Smith (Pitt) have a son Thomas born Nov. 20, 1677?

I am descended from Thompson Smith, b. @1750 Sussex County, NJ(?). I have seen several lineages showing Thompson as a son to James Smith and Anne Parke. This James is linked to Thomas, supposed to be son of Andrew Smith and Olive Smith (Pitt). Any information that corroborates this? Don Smith geowhiz1@gmail.com