I'm descended from the same couple on both sides of my family (three times -- that I know of) and despite the passage of a mere 400 years, there's no DNA trace of that relationship. The loss of half of the available possible DNA is actually what makes sexual reproduction more viable than, say, parthenogenesis, in complex multicellular organisms. :^)
Before doing any DNA tests, I watched some YouTube videos about the tests. One featured someone with well-documented American Indian ancestry but none showed up in the DNA testing. (I don't think that's the case with Elizabeth Warren--I think she was just fabricating the supposed ancestry.)
After five or so generations the odds of inheriting any DNA from any one individual in that generation is very small.
It’s a geometric progression. Two parents, four grandparents, eight great, sixteen great great, thirty two great great great. One thirty second is slightly over three percent, but of course you don’t inherit equal amounts from each grandparent.