Bible times starts from the beginning of time. The Bible is recorded history and prehistoric means before recorded history. Dinosaurs were in the Bible, and dinosaurs are often referred to as prehistoric, but they were recorded, so does all this mean that there is no such thing as prehistoric times?
Men typically assume that everything developed gradually over long periods of time. After all, our modern-day technology developed that way, so it isn't hard to assume everything happened that way. That is why it is assumed that ancient men lived in caves huddled around fires even though historical books like the Bible paint a very different picture of early men.
Prehistory means before recorded history. While the Bible does record in Genesis the highlights of the first two thousand years of world history, there is the question of when that history actually get written down. The Book of Genesis is counted as one of the books of Moses, so the question is did Moses record these events for the first time as told to him by the Holy Spirit? Did he take the oral histories of his people and guided by the Holy Spirit write an accurate copy of history? Or did he have access to historical records that are now lost to us and guided by the Holy Spirit compiled them into a book? I'm inclined to believe it is the later because of the wording in Genesis, but it isn't something I can say with absolute certainty. The point is that some could argue that while the Bible talks about earlier history, it wasn't recorded history until Moses (about 1,500 BC).
Not that it matters much. We have historical records from Egypt, Assyria, and China that reach back about about 3,000 BC, puts it near the time of the Flood. Since the Flood pretty much destroyed everything, you could say that prior to that is prehistory. Not that history wasn't being recorded back then, but that we just don't have surviving records of that period outside of what is found in the Bible.