I am avoiding calling the following three generations the 1st generation or the new 1st generation because I can't prove anything. The following information is speculative, on my part, and I hope it encourages some discussion among DAWES researchers.
What we know is that Thomas DAWS of the 1st Generation was born in 1769 Uckfield. This is supported by his death registration from 1843 which claims his age as 75. Although he was enumerated in the 1841 census, his age was rounded down to 70 so we can't use it to confirm his age and birth year. The 1841 census did confirm his birth location as Sussex and while he married and had most of his children in Kent, an 1809 Poor Law Removal Order directed the family back to Uckfield so that must have been his original parish.
Unfortunately, the Uckfield parish registers only go back to 1813 so are of no help in tracing the earlier generations. However, on my recent trip to Salt Lake City, I scoured the parish registers for the surrounding area and found a family of brick laying DAW's in Lewes which I like for his parents and grandparents. This is kind of like a jigsaw puzzle where some of the pieces don't quite fit and you have to push them in or hammer in some cases so here goes.
As you can see from the chart, the original 1st Thomas DAWS is in the 4th column with his children in the 5th column. I believe that his parents may be Thomas DAW and Mary HILTON who married in Willingdon in 1768 according to the Sussex Marriage Index. This supports Thomas' birth in 1769 as their first child. Thomas DAW was one of five children born to Joseph DAW and Ann EARL who married in 1735 Framfield. They had Joseph b. 1735, Abigale b. 1744 (big gap there) James b. 1746, Thomas b. 1746/47 and Susanna b. 1750. Ann EARL was born in Willingdon so there is another link to that parish.
I don't know where Joseph DAW was born but he died in 1752 Lewes and is buried there with a notation "At ye east end of Chancel Old Ground." This means that he must have been more than a general Ag Lab! My opinion! I haven't done any research in Framfield or Willingdon so that is work for the future. It is interesting that the given name Joseph was used by Thomas DAWES b. 1809 for his first child and Ann for his fourth child.
Now it gets very speculative with the parents of Joseph who may have been James DAW b. 1684 Warbleton and died 1761 Lewes who married Mary CHANNEL in 1706 Berwick. I don't know where Mary was born but she died 1752 Lewes. One of Joseph's sons, Joseph b. 1735, was apprenticed to James Sr. when he died in 1741 and the additional entry is added in the register "apprentice to James DAW Senior / OTP" (of this parish). I like to believe that James Sr. was his grandfather but he could have been an uncle of Joseph I suppose.
This takes the early DAW/DAWS/DAWES family back to 1684 where it will remain until I can prove or disprove the connections. As they say in genealogy, if you can't prove something then try to disprove all of the alternatives.