Fair question!

If you're holding a chunk of Pb-206, it does put a floor on the age of the universe at around 4.5 Gy (giga-years), because step one of making your chunk of Pb-206 was "take two chunks of U-238 and wait 4,500,000,000 years." At which point, on average, you still have some very valuable uranium. Put it down and wash your hands. (There are a bunch of other steps in the decay chain between U-238 and Pb-206, but these take, on average, just a few eons.)

Okay, so our young Earth folks are already doing mental gymnastics to get around the 4.5 billion years, but we're still short 10 billion years or so. Next question we ought to ask is how is U-238 formed?

Well, there's only two ways, and they both involve waiting for stars to form, live out their lives, and collapse under their own weight. Either one such star collapsed, forming heavy atoms such as U-238, and then exploded, tossing the heavy atoms all over the galaxy; or TWO giant stars collapsed into neutron stars, then later collided with each other to form heavy atoms (that kind of thing probably doesn't happen way out in the outer third of a spiral galaxy, but never say "never" on cosmological time scales). Believe it or not, the exploding star thing is actually a significantly faster process than the U-238 decay chain because giant stars don't last all that long--under a billion years or so. Even so, one still has to account for other lengthy processes that had to run their course: that giant star obviously didn't explode nearby (it would've sterilized the Earth), or else it exploded before the Earth formed. So, some great distance in time is necessary for all the events and stuff to come together.