Some self doubt is critical for right thinking.

some self-doubt is right for critical thinking

A system without introspection would never self-improve.

Does evolution introspect? did the universe evolve the gecko with or without introspection?

Evolution as a system does not improve, no. Evolution was superseded by self-improving (human thought-based) systems.

A gecko born did not self-improve. The species average offspring improved externally via natural selection.

> Evolution was superseded by self-improving (human thought-based) systems.

Strictly correct, but consider that our ideas are also going evolution. What we learn depends on our environment. We retain what's useful and don't what's not and we also pass it down through generations... This is pretty much natural selection, just at a different level.

“A gecko born did not self-improve.”

This might not necessarily be true, for example, a genetic defect that a gecko figures out how to leverage through self improvement (to feed itself) might then be passed on to offspring.