Bibles from that time period do exist today in museums. Even a second-century Latin translation of the Bible based on the Old Testament (Septuagint) and New Testament Greek has survived. The Catholic Encyclopedia calls this version the Vetus Itala (Old Latin), and says "Its New Testament is possessed complete in some thirty-eight manuscripts, but its Old Testament text has survived only in parts." Until Martin Luther the deuterocanonical books of the Bible were never omitted or put in a separate, non-canonical section of the Bible.
See the Catholic Encyclopedia entry "Versions of the Bible" at: www.newadvent.org.