There is sound scientific evidence that Gobekli Tepe is at least twelve thousand years old. And there are ritual imagery at both Gobekli Tepe and Easter Island, marking the Statuary at Eastern Island to the epoch twelve thousand years ago.
I still think the best proof of the Earths age being over 6000 years will come from the Gaia space mission. While I believe the other evidence is overwhelming, each piece by itself seems hard to completely understand. Do I know why astronomers are confident that the red shift of distant galaxies gives a good approximation of their age? Generally, maybe, but at some level I do end up just trusting their observations.
Parallax on the other hand is something we have all experienced.
Anyone who doesn’t wish to believe something will always be able to come up with a counter argument, but the contortions will be increasingly uncomfortable.