The Jewish people have been around a few thousand years, and were slaves, and lived in other countries throughout the world. How do I know with confidence that my ancestry is really Jewish? There must have been some intermarriage, & conversions throughout the centuries.
Rabbi Moshe Feinstein wrote (some forty years ago) that up until more or less the beginning of the 20th Century, Jews who were part of an organized Jewish community could be assumed to be Jewish and kosher to marry into any other community (because until that time, most communities existed more or less under the guidance of properly constituted Jewish courts). Members of later generations who were aware of direct lineage from such a family had the right to assume that they too were kosher. The main problem is that, as we can plainly see, there is more and more confusion and ignorance in the Jewish world and things are far from clear.
In any case, if your family has been free of such doubts for the past century or so then you can assume that all legal issues were properly dealt with in all previous generations. Even if there was some problem that has since become hidden, Jewish law doesn’t consider that a factor that’s pertinent in any practical way.
Rabbi Boruch Clinton