No, that is 100% not how evolution works. No individual has ever laid an egg of a different species. One mutation doesn’t make a non-chicken a chicken. Chickens evolved from their ancestors slowly over many many generations. It’s like how you can’t change one word and make a language a different language, but if you change enough words, it becomes a different language.

Let me put it another way. If you take a modern chicken back in time 10,000 years, it could probably breed with a chicken from then. But if you take it back maybe 20,000 years, maybe it can’t breed with a chicken from then. But if you take the chicken from 10kya, it could breed with the chicken from 20kya. So are they all the same species? Are they different species? Are they all chickens?

Humans like to put things in little boxes with clear delineations, but that’s not how nature works. Species don’t come to be from one mutation. They evolve as the accumulation of many many mutations over many many generations. There’s no point at which you can say that child is a different species than their parent.