The koan implies chicken egg, though, not any old egg.
Did the proto-chicken lay a chicken egg which hatched the first chicken, or did the proto-chicken lay a proto-chicken egg which hatched the first chicken?
There is this implicit bias in your question that complexity comes from a discontinuous change which can be noticed at one moment, it’s much more diffuse and gradual. Just like we won’t know we are in World War 3 for another couple years.
If a chicken egg is an egg laid by a chicken, the chicken came first
If a chicken egg is an egg that hatches into a chicken, the egg came first.
We know that the first case is correct because an unfertilised egg laid by a chicken is called a chicken egg despite by definition not hatching into a chicken.
Therefore the chicken came first
I guess it depends on whether the crucial mutation that flipped the organism from "non-chicken" to "chicken" happened before or after fertilization!
Or alternatively we can say that the germ line went from 49% chicken to 50% chicken to 51% chicken? Biology is really a continuous state space anyway and trying to push things into categories too hard will break them.