The Septuagint was written about 300-400 BC. It was translated directly from Hebrew to Greek by the 70 translators (LXX). This copy was available to everyone including Jesus and His Apostles. Of course, the Jews could read the original Hebrew, so they didn’t need it, but everyone spoke Greek at this time. The NT was written in Greek to begin with. Any Latin translation would have come from Greek.
Certainly if you're talking about the NT. As far as the OT is concerned, I don't think St Jerome (who translated the Vulgate) exclusively translated the LXX. I'm pretty sure he had at least some input on the original Hebrew from rabbis.
Jesus did not speak Greek. He spoke Aramaic.