From censuses it is apparent that Sarah Oliver was born in Hoo, Kent.
This could refer to St Mary Hoo or Hoo St Werburgh which are a few miles apart.

There is a baptism for Sarah Oliver at Saint Werburgh Hoo in 1787 which gives her parents as Thomas and Mary Oliver.

Thereore it seems fairly certain that Sarah's mother was called Mary but at this stage her surname is not known.

One of the witnesses at the  wedding of Sarah and John was Mary Oliver which was presumably her mother, or possibly a sister named Mary.
  

        The following are baptisms of children to Thomas and Mary Oliver in Kent
        Sarah was baptised in 1788
        Thomas - 15 Aug 1780 Snodland, about 9 miles south of Hoo.
        William - 28 Aug 1786 Maidstone, about 12 miles south of Hoo
        Elizabeth - 28 Aug 1789 Maidstone
        James - 21 Mar 1790 Chatham, about 5 miles south of Hoo
    

When I (David Phillips) was younger we had a Dictionary inscribed
Mary Oliver  MDCCLVIII
The year is therefore 1758.
It seems unlikely that this person was Mary the mother of Sarah unless her maiden name was also Oliver or she herself in later life included the date of her birth.
It seems more likely that Mary was a relative of Thomas, possible his mother.