“ The man who asks a question is a fool for a minute, the man who does not ask is a fool for life.” I understand that based on Halacha a Jew is only a person with an unbroken Jewish Maternal Line but how will someone know that his maternal line is unbroken from Sinai ?
Your question is correct. We don’t “know” that it indeed not broken, as we unfortunately don’t have written account of exactly who each person’s mother was for the last 3333 years since the giving of the Torah. Unfortunately the Jews have been exiled numerous times and there was a lot of upheaval. However each generation knows that their mother and grandmother were Jewish, and they pass this on to their children. There were times that towns kept a written record of ancestry, which was helpful in this regard. Otherwise we have to rely on the fact that if it was understood until now that this person is from Jewish ancestry, then we assume that indeed it is so.