“On the one hand, scholars argue no Jewish tradition about a messiah suffering shows that the Church added this idea. And once you show a document, an ancient document to point to, showing that they did interpret a prophet like Daniel to expect a suffering messiah, well then people say ‘Well this proves Christianity can’t be true.’”

The suffering savior is a Pagan motif and so isn’t original to Judaism as far as I can tell from my studies. However, that isn’t to say that earlier Jews didn’t incoporate the suffering savior motif prior to some later Jews who became known as Christians.

As an example, allegorical interpretation originated from Greek thought. Allegorizing the Bible was done by the Jew Philo before Christianity. Numerous Christians used Allegory in the same way towards Biblical passages such as Genesis. Did the early Christians get their use of allegory from Philo who got it from the Greeks or did the early Christians get their use of allegory directly from the Greeks. Most probably it was both. All of these various traditions were mixing together for centuries before and after the beginning of the Common Era.

So, the important part is that the suffering savior, like allegorizing, is unoriginal to both Judaism and Christianity.