Pokémon "evolution" exists and is called metamorphosis
Real world animals do this. However, it's not called evolution because it is not in any way evolution; it's metamorphosis, and rather than "experience", it is food (or sometimes just time) that must be gathered to begin the process.
The caterpillar $\to$ butterfly is pretty much exactly like pokemon evolution (which is probably why this real life metamorphosis inspired Caterpie $\to$ Metapod $\to$ Butterfree).
More examples would be
Tadpole $\to$ Frog
Maggot $\to$ Fly
There are huge numbers of examples of metamorphosis, although caterpillar $\to$ butterfly is one of the most extreme. Generally, they include 4 stages: egg, larva, pupae, adult.
Why is this not evolution
Evolution is change in heritable traits of biological populations over successive generations resulting from a selection pressure in their environment (where "environment" can take a very large definition).
Baby Pokémon are the lowest stage of Pokémon evolution. The concept
was introduced in Generation II, along with breeding
So we can see that Pokémon evolution is not heritable, baby Pokémon are always born at "the lowest stage of Pokémon evolution".
Equally Pokémon evolution always follows a set "plan" (of one of a small number of plans) so the "design" itself cannot be driven by a selection pressure in their environment.
Finally Pokémon evolution occurs for a single individual so is not over "successive generations"