Christian here with 4 year, fully accredited bachelor degree in Biblical Studies (meaning I've spent a little time thinking about this academically). I'd humbly like to add to to the conversation:

You'll find that it's a vocal minority that hold to "Young Earth Creationism" (earth is less that 6k years old). Think of it like the Tea Party minority that is bugging up the House of Representatives at the moment. Many well studied men and women of faith don't believe that the earth is that young; one professor of mine with a doctorate in theology was an unashamed Theistic Evolutionist (meaning he was of the mind that evolution as popular science posits is true and that it was set in motion by God. He did not see it in conflict with the Christian scriptures).

This goes along with Carbon Dating for some though a few that I have talked to don't like CD not because it doesn't match what they believe but because there have sometimes been irregularities (the claim is that some dating done after the eruption of Mt St Helens in 1980 gave false positives of deep time when it should not have - I'm not a scientist so I can't comment on that).

As to your last statement, it is true that a large part of Christianity is based on faith. However, "blind" faith is not common in academic circles and having at least some foundational ground to stand on is quite important. Sort of an evidence first but willingness to take the unknown on faith until further evidence can be found (a standpoint taken by many in non-Christian circles including science: "I have this theory, the limited evidence I have accumulated supports it but my hypothesis remains the same until I can get more evidence".