Well, that’s one fundamentalist interpretation of the Bible. There are others. There are legitimate sources that state that dates and times before the Sixth Day are not to be understood as we know them today (which makes sense – what is a “day” before there is an Earth and Sun, for instance.) ~6000 years since the first civilized human beings is far more believable than 6000 years since the big bang. (Some date the oldest human artifacts to about 9000 years ago, but not much further than that.)
I’ve also read a very good essay about how the 6 days of creation is not literally describing creation of the world, but how it is an allegorical description of God’s creation of prophecy in the world – how He took a merely biological creature (some early human – which could be descendant from apes, for whatever that is worth) and gave him a divine spirit capable of receiving prophecy, with Adam being the first.
The Church may disagree with these theories, but the Church is not the final word on how to understand the Bible (unless you’re Catholic, of course.)