OK, why would that first cell develop into an egg then instead of the organism that lays
First you have multicellular organisms evolve. All of them reproduce by producing a single cell copy of themselves.
Over time, you get more advanced multicellular organisms, all of them reproduce by producing a single cell. (edit: by the way, single cell to multicell development has been observed in research, by accident. I think it was yeast that suddenly showed multicell behavior, or something.)
Then, the sexual reproduction evolves where two organisms of same kind share genetic material. One provide one part, and the other the other part, and somewhere at some point, the cells they shared evolved to be different, gender specific. The ova is a cell and so is the sperm. Probably some earlier forms of ocean animals, fishlike, perhaps.
Then you had land animals evolve, and they split up at some point, and mammals evolved to keep the egg inside the mother during gestation, while other animals buried eggs with thin shells like turtles, and other evolved to produce harder shells for the gestation to be protected.
Later on, birds evolved, and at some point one of the birds was domesticated and later named "chicken".
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Think about this, dinosaurs existed before the birds, and we have fossilized dino eggs. A few of them even have embryos.