Cesium-137 is made in nuclear reactors, but some radioactive isotopes with shorter half lives (well, short compared to the age of the Earth) exist in nature because they are a product of the natural radioactive decay of other, long-lived materials like Uranium.

You are correct. It can't. It is made: https://en.wikipedia.org/wiki/Caesium-137#Uses

"As an almost purely human-made isotope, caesium-137 has been used to date wine and detect counterfeits and as a relative-dating material for assessing the age of sedimentation occurring after 1945."

It hadn’t survived for billions of years, it was made of caesium-137 which was manufactured in a nuclear reactor.

It took us a few hundred years, but we did finally realize the alchemists' dream of transmuting elements into other elements. It's just a little expensive.