I've discovered that many are in my situation. My trail back to the past stops at my (paternal) grandfather and it picks up again through an auDNA test (ftdna.com in this case), and people here have told me that these can't be connected. On the other hand, the existence of a cousins chart (3rd or 4th cousin in my case, like many others) could with A LOT of PERSISTENCE lead to one of many out there. I know, for instance, that my GM Anna Berg coupled with someone, probably in Frankfurt and only somewhat less likely in Karlsruhe Germany on roughly 10 April 1906 If her baby, my father Rudolf Berg, was born precisely on "schedule" (and what baby is?).
So finding this Unknown Jewish teen (her age at 16 or a little older) or attractive older man (possible) or a rapist (an ugly thought but anything is possible because Anna was essentially orphaned. By the weeks preceeding his birth, she probably lived in a town that wasn't her birth/home-town (Karlsruhe) where she had only more distant relatives but not immediate family, who had in the main died). It's possible her maternal gm Rosa (Rosalin/Rosalia) Baer lived in Frankfurt at the time (or Rosa's relatives). By the time Rudy was 3 months old, Anna took him to Baden-Baden to live with Rosa. Anna went immediately to the US where a relative of Rosa had paid for her passage. Anna arrived with $10 to purchase a train ticket to CT, where Veronika Schmid lived in New Haven. Anna got a job as a live-in nanny. (& that's ALL I know.)
WE need to find our UNKNOWNS. Need I say more.