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Long ago when I was a child, I was taught to believe in young earth by the lectern thumping clergy. The world is only x, typically six but maybe a few more or less thousand years old, because that's what the Bible says.
Children have no ability to discern truth from lies, so that's all there is.
I didn't really feel as though I had a proof of how old the Earth was, until I started thinking deeply about thousands of different topics and trying to separate truth from lies in an algorithmic way first assisted by paper, then later by computer code.
One of the arguments that did it in for me, is a photograph of the Sahara Desert. The fact that there are millions of cubic kilometers of pure river-sand there. One may ask: "how did river sand, which can only be created in rare conditions at the mouth of rivers, accumulate in the sahara desert. The answer comes back, well, you see there was a river in Europe that was really good at producing sand by mountain erosion, and the med sea aggregated this sand. But you see the mouth of the med opened and closed at least a thousand times in the last 2 billion years, and when that happened, the wind would simply blow all the sand from the med south into africa which was blown west, then east, then west again, stuck there forever, and now you have billions of cubic kilometers of circular river sand in Africa, an impassable barrier superior to any erected wall, and if you dig down a mile deep, you will find additional billions of cubic kilometers of "compressed circular river sand" called sandstone. And under that, you have "deep slate" which is compressed sandstone.
To say the Earth is motherfucking old, is understatement of the year.
The Earth, pause for dramatic effect, is older than you can even wrap your brain around. It's so old, that if you zoom out to bring that oldness into view, then Humans don't even exist.