Not 2000 years ago. I would guess that neither Jesus nor any of the apostles spoke latin, save Peter and Paul (and that after they had come to Rome).
The early masses were in the vernacular. Which would be Greek, Aramaic, Syriac, Egyptian, etc.
As Christianity spread, it was still in the Vernacular. In the West, that was Latin. Everyone understood it. (French, Spanish, Italian are all dialects of Latin). The mass was not frozen in that language for centuries. Finally at Trent it was specified that Latin Rite masses would be in Latin.