Well, it's been proven many times, but just for starters - ancient commentaries on the Scriptures were written in Aramaic. Both the Babylonian and Palestinian Talmuds were written in Aramaic. The Syrian Orthodox church is still using it in their liturgy.
There was even an Aramaic Galilean dialect (which is probably what Christ and his disciples spoke.) Bits of it are scattered around the New Testament. But they did NOT use Hebrew - most Jews of the time did not. Hebrew was read and written almost exclusively by the priestly class in Jerusalem. Most people heard it during services but didn't understand it very well (sort of analogous to the use of Latin in the Catholic church pre- VCII.) That is why the Septuagint was written (and why it was necessary.)
I thought you might find this article interesting, because while the author is actually arguing about something different (responding to Muslim criticism re the accuracy of the New Testament), he answers your question fairly directly and with supporting points. Excerpt:
The Jews of NT times spoke Aramaic at home and in conversations. Aramaic was similar Hebrew and Arabic. (al-Rahmaan, al-Rahiim, in the Fatiha of the Quran were probably derived from the Aramaic language). In business life and official writings they used the common Koine Greek that all peoples in the area used for hundreds of years. They actually thought and talked in at least two or three languages as people do today.The Roman occupiers of the Holy Land at that time spoke Latin and Greek. Evidence of the three languages used in that time is found in the New Testament itself in the Gospel of John 19:19-20:(NIV)
"Pilate had a notice prepared and fastened to the cross. It read: JESUS OF NAZARETH, The King of the Jews. Many of the Jews read this sign, for the place where Jesus was crucified was near the city, and the sign was written in Aramaic, Latin and Greek."There are other evidences such as "talitha cumi", little girl arise, and "maranatha" Lord come, in Aramaic. These show that the people were multi-lingual. Greek was the main means of communication but the heart language of the people was Aramaic. The language of formal worship was Hebrew, most likely with Aramaic interpretation and explaination. The New Testament and Gospels, which were written for Jews scattered all over the Mediterranean world were naturally written in the common language of Koine Greek so that all could understand and benefit. Koine Greek was much more expressive and more easily translated into western Latin based languages and therefore the entire world benefited.
Prove it
What ancient commentaries? Eusebius written in Aramaic?
Jerome written in Aramaic?
Chrysystom written in Aramaic?
Babylonian Talmud would have been writen before Jesus and would have been written for the Jews who never came back from the captivity, so that has no bearing on this conversation.
The Septuigant was NOT written for the underclass, it was writen because 70 men took to translating the Hebrew into the language of the conqerors while they lived in Egypt, the Greeks, in order that the Jews who were scattered around the world would have the Word of God in their new Language.
But Multilingualism does not mean that Jesus didn't speak in thelanguage that Abraham spoke of, in fact, if He spoke a DIFFERENT language than Abraham, Isaaac and Jacob and David, He would be most out of place.