i don't know that a genealogist would find proof. I don't see any record of Benjamin Hawkins marrying in Hall, GA. If he married in SC, there are few if any marriage records there. The only chance of proving it would be a probate record or will for Benjamin Hawkins or a church record of the marriage and they may not exist.

I think your best chance would be a yDNA test. If a male descendant of Tyre Hawkins tests and he matches descendants of Matthew's family for example, he would be correct that Rebecca was the wife of Benjamin. If Tyre Hawkins was the illegitimate son of Rebecca Hawkins, her descendants' yDNA would not match Hawkins, but it is possible they may find the surname of the father.