Some radioactive isotopes have been here as long as the Earth, and we’re just “starting with what’s left”. Uranium is the 48th most abundant element on Earth and takes billions of years for half of a sample to decay. Potassium-40 is common enough that you can detect it in all bananas with a Geiger counter, and it’s half-life is 1.25 billion years old. Most of our supplies of isotopes like these are “old”.
Some radioisotopes are produced when other radioisotopes decay. There’s a Cesium-131 that’s produced when Barium-131 decays. It’s half-life is 9.7 days. Iodine-131 is produced by nuclear power plant fuel and has a half-life of 8 days. So these “daughter isotopes” are typically either detected as part of an ongoing process, or manufactured intentionally for use while “fresh”.
Some radioisotopes are created in the atmosphere by lightning or cosmic radiation. Nitrogen in the upper atmosphere can be turned into carbon-14, which can become carbon dioxide and apples and people and everything else that carbon-12 can become. It’s not terribly rare, and it takes 5700 years for half of a sample to decay. But it’s always being replenished in the upper atmosphere.