There is scientific proof that the egg came first
The chicken is descended from other types of birds, and there is scientific proof to show that the first egg was laid by another bird, which eventually produced what we now know as a chicken.
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At a point in the evolution of birds, an almost chicken-like creature experienced a genetic or evolutionary mutation and managed to produce the world’s first egg that hatched a bird that was, by modern standards, a chicken. This follows the Darwinist theory of evolution that most biologists have accepted to be true. The way most modern species have developed and the way we have acquired our specific genetic traits as a species are through slight genetic mutations that, over time, have accumulated into the creation of a new type of species. In the same way, the modern chicken developed from slight genetic mutations that added up to evolution. This must mean that the egg came first, because the final mutation that put in place the modern chicken was not a mutation in the hen herself, it was simply a mutation in the genetic traits that were passed down. Therefore, the first independent organism to carry that trait would have to be the egg that hatched the chicken.
If the Darwinist theory is true, then the first chicken must have only existed once the chicken was hatched. When a chicken is still within its egg, it could technically be counted as a fetus or an embryo, not as an actual chicken. If the first chicken came to be with the birth of the genetically mutated bird, then that chicken was only born after it was hatched from its egg. Therefore, the starting point would originate at the first chicken, making the chicken come before the egg.
[P1] The first chicken came to be due to a genetic mutation of another type of bird evolving. [P2] That first chicken must have come from the genetically mutated egg laid by a different bird.
Rejecting the premises
[P1] If the Darwinist theory is true and new species start at the conception of a genetic mutation, then that genetic mutation only exists after the first chicken is born. [P2] Living beings can have changing genomes throughout their life, so it is still possible that the mutation happened within a chicken's life.