Hi,
No one seems to have information on Matthew's parents, however there are a couple of things I think I have uncovered. One successfully which is the marriage bann in Lannivett (which could be Lanhydrock) 27 Mar 1715 of Matthew and Mary which confirms her father as John Bullock. There is reference to John Bullock and Elizabeth Hambly with children and Mary being the youngest although Elizabeth's dob puts her at over 50 when she had Mary so I am not certain that her dob is correct.
The second is that there are a group of Poads, with several Matthews, a couple of Johns, a Henry, Joseph and a Mary all registered in the St Mellion, Cornwall parish. St Mellion is only a short distance from St Dominick and Callington.
If these are ancestors and relatives of our Matthew, I think they would be cousins descending from Matthew's un-named grandfather. Estimating Matthew's birth year as c.1688 (Mary Bullock is 01 Nov 1690), his father would have been born about mid 1660s and his father about mid 1640s.
From the St Mellion register, a Matthew Poade is baptised 1697, Henry 1690 and Thomas 1700. These are the sons of Matthew Poade and Susanna. Matthew would have been born about 1670 which would calculate him to be the uncle of our Matthew.