Simple proofs of the age of the universe (or other things)

I saw some time ago Carl Sagan asked schoolchildren for proofs that the earth is round. I can no longer find it, but they gave him sound, simple answers. One was watching a ship seem to sink below the horizon as it grows distant. One was photos of Earth from space. One, I believe, was seeing how the sun may reach the bottom of a well in the tropics, but not further north.

I’m trying to find similar answers related to the age of the universe. I’ll operationally define “old” as “older than human history.” So far:
* We know by parallax distances to various stars within 300 l y, and can tell from their distance, color, and brightness how bright a star of a given color should be. So if we see a further star and measure its color and brightness, we can deduce the distance and thereby how long it took the light to get here. (This is more complicated than I’d like, but oh well.)
* If the universe started X thousand years ago, wouldn’t we be seeing more stars appearing every year at the X-thousand l y range?
* There is a star that exploded? did a nova? and some decades later its light illuminated a nearby nebula. By the time it took to illuminate, we know the distance between star and nebula. Since we know the angle, we can get the length of the other legs of the triangle, which are further than light could travel in human history. (I can’t remember the name of the star, alas.)
* Carbon dating.
* The Grand Canyon’s sedimentary layers.
* South America and Africa look like they fit together. If they traveled at current speeds of continental drift, they couldn’t have reached their current distance in a few thousand years (plus, their animal populations would have mixed when they were touching).

What else?

It’s interesting to think of how this works on other questions. Germs, or spontaneous generation of life? proved by canned food. Oxygen, or phlogiston? proved by a sealed-up candle. Quarks?