Christians and Jews at same time period?

Jews had been around for a long time before the Christians. So, the Hebrew Bible came first.

A couple hundred years before Christianity began, a Greek translation of the Bible was produced at the demand of Greek emperor Ptolemy. This translation was viewed as inferior by the Jews because of the layers of meanings lost in any translation, but especially of the Torah where every letter has significance. As Christianity spread among the Gentiles, the Greek version would have become the standard in Christianity pretty much by default, since it was more accessible and the converts were essentially people who wanted to accept more Jewish ideas without the intensity of study and practice that was standard among the Jews, thus the Bible in its original was not as necessary and the Christian New Testament was even originally written in Greek. Today, there are numerous Jewish translations of the Tanakh, or Jerusalem Bible, however these generally are printed in a bilingual format - Hebrew on one side, English on the other - with the idea being that the English translation is merely a guide for those who struggle with the original Hebrew.