The Bible does not contradict with science that the earth is millions of years old. But how long have people been on the earth from the time of the first man Adam? We believe based on Bible chronology that it is around 6,000 years. Neanderthals and other non-human animals with human-like traits could have been in existence prior to Adam and Eve, as animals were created by God first. They could have continued to live simultaneously with humans as well.
Human DNA is passed down from both mother and father. Mitochondrial DNA, however, is only from the mother. The current scientific presumption is that all human mitochondria descended from a single mother. Ironically, this one female ancestor has been dubbed “Eve” or “Mitochondrial Eve.”
Neanderthals had mitochondria like every other living creature who is not bacteria, but their mitochondria clearly were not from “Eve.” Therefore, they are not human but are animals, created at some point according to the book of Genesis. They may have lived at the same time as humans, which would not disagree with the biblical record.
We refer you to an article called Eve, the Mother of Us All, for more explanation.
In trying to make them sound human, much is reported that Neanderthals acted in similar ways as humans, such as evidence of flower remains found at a Neanderthal burial site. However, grave practices are not just human, so Neanderthal practices would not automatically put them in the human family. Elephants revisit the bones of their dead and scatter them around. Dolphins and chimps handle their dead with respect and mourning. The records of dogs mourning for their owners are replete with touching examples. The Australian Bower Bird males arrange the nests with an eye to design, color and introducing shiny objects from civilization. These are not signs of being human.
The oldest ACTUAL human is debatable. Of course, creationists are looking for a number around 6,000 years to correspond with the biblical record. As one can imagine, this is a complicated subject. Historically scientists have said humans lived hundreds of thousands of years ago, but there are admitted problems with the dating and recent hypotheses are getting closer and closer to that 6,000 figure.