When it comes down to it, everything is faith. I have faith that I am chatting with somebody who is calling himself AppyPappy, but for all I know, this is really a Turing test.
All indication are that, from Sinai forward, that is one the Jews were really good at and that was keeping the Sabbath. Even during the Babylonian captivity, the Jewish people who were allowed to stay in Israel kept the Sabbath and were able to teach it to those that returned.
There’s no historical that I am aware of that contradicts that one fact.
But your belief is not in the actual Sabbath day. Your belief is that the Jews are doing it right. That’s the problem with throwing all your trust on it. Not only that, God didn’t tell them which day. Moses set the Sabbath before he got the 10 Commandments (Ex 16)