Europa, one of Jupiter's moons, is 4.5 billion years old (like Earth.) However, its surface is only 20-180 million years old. What could lead to a planet/moon's surface being younger than the planet/moon itself?
In short, you need a process that keeps renewing the surface.
One of the reason is plate tectonics. For this very reason also Earth surface is younger than the planet itself, and finding very old rocks is very difficult.
Heavy meteor bombardment can be another reason, rejuvenating the entire surface.
There's a difference between material age and appearance age
@L.Dutch is absolutely right about renewing the surface. (I upvoted his answer). In that case, the material age of the surface (e.g., how long those materials have been on Europa) is the same as the planet, but the appearance age is much younger because the appearance regularly changes. What are the most common causes?
- Plate tectonics
- Fluids, especially water
I'd like to address the idea of material age. There are ways to rationalize the idea that the material on the surface is younger than the material in the core. In this case, the less active the planet (ideally, no wind, tectonics, volcanism, or fluids) the easier it is to rationalize a young material age.
- Cosmic dust
- Merging planets (bit catastrophic, this one)
In this case, it's the source of the material that's the bigger issue: a comet that degrades with each pass near its sun, the remains of a planetary body (think, "like our asteroid field") or the sweep of a nebula that hasn't yet been fully consumed during star formation.
Note that we're talking geological time scales here. Nebulae aren't all that dense, but they're quite a bit more dense than open space.
However, your bigger problem is explaining how you know that the surface is younger than the core
Let's assume a planetary body with no atmosphere at all. It's small enough to justify the inability to keep one. How do you know if, e.g., constant bombardment from Leonids-style meteors created a younger surface than the core? Without the chemistry of an atmosphere, it's a bit harder, but not impossible.
Carbon-14 dating is only practical for ages up to about 50,000 years and works because cosmic radiation keeps carbon-14 quantities in the atmosphere fairly constant. In other words, "fresh" carbon-14 is absorbed into things fairly constantly and we can look at its decay compared to "today" to calculate an age. But you need a source of carbon-14 for this to work and with the wrong atmosphere (or without an atmosphere) this solution can't be used. Besides, for the most part, it's only really practical to date things that were once alive.
Potassium-argon dating can date volcanic materials ranging from less than 100,000 to more than 4 billion years old.
Rubidium-strontium dating can be used to determine the ages of items ranging from a few million to a few billions of years old.
Uranium-thorium-lead dating is the most useful for the oldest objects due to long half-lives and predictable degradation to lead.
Luminescence dating exposes long-buried geology to light to determine how long the geology has been buried.
All but the first of those tests could be used to rationalize knowing the age of your surface and core.
It's worth remembering that from a simplistic point of view, all atoms are the same age (kinda)
It's perhaps more accurate to say that all electrons, protons, and neutrons are the same age (at least the word "kinda" is less applicable). Atoms are involved in chemical reactions that changes atomic structure. Thus, in a star hydrogen is slowly turned to iron. But those electrons, protons, and neutrons have (basically) all been with us since the Big Bang.
In other words, you're measuring dates from the last big event. For the age of a planet, the last big event was planetary formation, meaning that a lot of (e.g.) carbon has been sitting there in a big ballish shape for a honking long time. But the stuff that impacts the planet to change the surface's material age has also been around a long honking time... but it wasn't sitting atop all that carbon, etc.
And that makes all the difference.
OK, I've been rambling...
You can change the appearance age by changing the surface without changing most of the mantle (what I've been calling the "core" though this answer... but the core's involved, too).
You can change the material age by depositing mass onto the surface that wasn't part of the original planet-forming process.
Imagine that... even on cosmological scales, things get dusty.
In the case of Europa, but also Io, tidal forces from Jupiter's gravity cause internal heating, leading to increased volcanic and tectonic activity. For instance, Io is the most volcanically active body in the Solar System due to Jupiter's gravitational pull.
Similarly, the tidal forces on Europa lead to significant heating of its interior. This heating is believed to maintain a subsurface ocean beneath Europa's icy crust. The continuous flexing of Europa's surface due to these tidal forces also facilitates the cracking of its ice layer, which explains why the surface is younger than the moon.
You can read more about this phenomenon here.