So, Derek Abbott believes that the Somerton Man is the biological father of Jestyn's son Robin. Extraction of the Somerton Man's autosomal DNA won't be possible though until the South Australian Attorney General gives his official approval for an exhumation. This form of DNA could allow us to find the Somerton Man's "cousins" on a genealogical database. (This is how experts find the birth parents of adopted children -- by triangulating the family tree from DNA cousins.)
Samples of the Somerton Man's hair exist in a museum, but unfortunately concentration levels of viable autosomal DNA are too low in such old hair. As an initial test, The University of Adelaide team successfully determined that the Somerton Man's mother belongs to DNA haplogroup H.
Sadly, Robin died of prostate cancer in 2009. He was cremated, and so his DNA is unavailable. However, Robin's DNA profile has been obtained indirectly by 'subtracting' the DNA of his spouse, Roma Egan, from his daughter (Rachel Egan) this is called phased DNA.
A DNA heritage admixture test shows that Robin possesses a small percentage of Amerindian. Robin's maternal line is well-documented, and so this result points to a paternal American line.
By scanning genealogical DNA databases, it turns out that Robin has a large number of cousins in the USA. More significantly, 40 of the closer matches tend to have roots in Virginia. Some of these are connected to Thomas Jefferson's tree who consistently match with Robin on Chromosome #8. Remarkably, Robin is within the 3rd cousin range to a direct descendant of Jefferson's grandfather, Isham Randolph.
Of course, there is further research to do and the hypothesis that the Somerton Man is American needs further testing and verification. The current overall evidence is sufficiently compelling for investigators to focus efforts on the USA as a key to this puzzle. For example, searches of US-Australian ship's passenger logs, for the 1940s, now become a tantalizing line of inquiry. 
Ok, so DNA and genetics is clearly not my strong suit, but I'm already confused.
Autosomal DNA and Genealogy: https://www.youtube.com/watch?v=Jtpe6u2J5ps