There are atoms for which we believe they are stable, although they theoretically could decay. But we never observed it.
Bismuth-209 was for a long time considered to be the heaviest stable primordial isotope, it had been theorized for a while that it might technically decay, but no one proved that until 2003, it has a half-life of over a billion times the current age of the universe, and so for all practical purposes can be treated as if it is stable.
I’m no physicist, so I very well be way out of my element, but I would personally not be the least bit surprised if it turned out every atom was technically unstable, but since the decay is so incredibly slow we may never be able to accurately detect it. Using the lead-209 example you gave, if it ever is proven to be unstable, the half life should be at least 10^25^ (10,000,000,000,000,000,000,000,000/ten septillion) times longer than the age of the universe. Smarter people than myself probably have some ideas, but I couldn’t imagine how you could possibly attempt to measure something like that.