Explain 'dem bones, holy homey

Here’s a question for any Christians who believe everything in the Bible is true (I’d call them “fundamentalists”, which was what they used to call themselves, I believe, but the word has a negative association these days):

What about Neanderthals?

If you believe in the Bible, including Genesis, you believe in Creationism, and that means that such a thing as “cavemen” could never have existed; the first men in the Bible, both in Eden (Adam and Eve) and shortly after (Seth, Cain, Noah and so on) are described as civilized, having a society, building cities, and so on.

So, according to Bible-based Creationism, there never was such a thing as Neanderthals living in caves, being more advanced than apes yet less than men. Not to mention that they are supposed to have lived millions of years ago… hey, isn’t the universe just 6000 years old?

But… where do all these fossils come from?

Logically, a Christian would have to accept one of the following:
1. The fossils are all fakes, created by scientists and other “enemies of faith”, to discredit Creationism.
2. God created the fossils to “test our faith”, making them appear much older than they really are, to all scientific tests - not to mention the fact that they are from beings that never actually existed.
3. Genesis is, at least in part, a fictional book.

So… which is it?