It’s the same question when an advert says a watch loses one second every 30 years and the watch just came out. How do they know this when the watch isn’t 30 years old!?! They don’t wait 30 years. They have extremely accurate clocks and see how much the watch varies after a few seconds or minutes.
So if the watch loses 0.00000000000579174282808486 seconds every minute, then you can say the watch loses 1 seconds every 30 years.
Similarly for Uranium. The half life is how long it takes for 50% of the uranium to mutate. So just look at how much of the uranium mutates in 1 minute (or whatever) and extrapolate and assume that it is totally stochastic process.
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