Our life-time is negligible, compared to that of unstable nuclei with half-lives of billions of years.
How, then, are these half-lives estimated, if you may never even witness a decay. It's like estimating the probability of a popcorn kernel popping, after one of the 200 in a pan has popped.
Would it be done over, say, a decade, with a massive amount of the source constantly monitored by a gygameter? Wouldn't the data still be inconclusive?
Is it estimated other ways, such as by examining the relationship between the composition of an atom and its half-life, to extrapolate larger half-lives? Comparing the quantities of the nucleuses isotopes found in nature, to extrapolate?
-- How on earth could scientists know that Lead-204 has a half-life 10,000,000 time longer than the age of the universe ~14,000,000,000 so: 140,000,000,000,000,000 years.