IIRC, it's roughly 14 billion years or so. Earth has been around for I think 4 billion. Humans for around 10,000-ish. That number may be off, but it's well under 100,000. We, as a species, have gone from crudely drawn shapes on caves to starting to explore beyond the bounds of our planet.
The claim is that our journey into the stars is inevitable. That we will begin to colonize other planets. And that this colonization is exponential. To illustrate let's say tomorrow we know how to do it. The only issue is the time it takes. Let's pretend we can do it in 10 years. From nothing to fully functional, autonomous human colony in 10 years. Technologically equivalent. Which means that colony is also capable of sending out colonies. So now instead of one planet sending out colonies, you have two. Then four, then eight, and so on. Basically, every 10 years, you would double the number of planets inhabited by a species. In just 100 years, there would be 1024 planets supporting human life. In 1000 years? 100 cycles of colonization? 1.2e+30. Huge. There are "only" 40 billion planets that seem habitable in our galaxy. We'd have run out of planets to colonize at the 36th cycle. And even if it takes 100 years to colonize a planet to the point where they're just as capable, you're just really shifting the decimal one point. That's 3600 years to a fully inhabited galaxy. Cosmically, a blip in time.
So, the Fermi paradox says that given that colonization of other worlds is inevitable for an intelligent species, if life and human-style intelligence aren't unique, why haven't we seen evidence of other civilizations yet?
Either been contacted, run into an artifact of some sort, or found some sort of signal.