How could evolution produce immortal beings? The more "immortal" an entity is, the more likely it is to lose the race with quickly evolving short-lived entities driven by natural selection.

So an immortal being would have to be able to self-modify in order to remain competitive. But that's only possible if it's able to run internal models of itself and subject them to simulated natural selection.

In other words, create mortal beings in its own image.