Tree-ring dating or Dendrochronology is a reliable, scientifc way of determining the age of trees and, if you combine the results, of the miminum age of the earth.
And guess what? The trees whisper to us that they alone already can refute the myth of the earth being less than 6000 years old. In fact, we can prove, not using carbon or any type of dating, that the earth is at least 11000 years old!
Of course, the earth is way older than that, but that would already border on heresy... No, seriously, we just don't have an unbroken record of trees beyond 11000 years ago, so we can't go back further than that (in the meantime).
Credits: YouTube user cdkoo7. This video can only be found on Dnatube due to featuring music from Sony Music Entertainment (The Final Countdown, by Europe). If the logo in the top obscures viewing, just switch to fullscreen using the icon in the bottom-right.