The chicken vs egg question has never been about chronology or science.
It’s been about religion vs science.
Science says the egg came first: something nearly imperceptibly not quite a chicken laid an egg that hatched a chicken. That’s how evolution works, with the egg coming first.
Religion says a god poofed a chicken into existence. The chicken came first, and only ever laid pure chicken eggs. The eggs will forever hatch a chicken and nothing but a chicken.
That’s the chicken vs egg thing. It’s not a puzzle at all, it’s just science vs religion.
e: simplified. I’m too wordy by default.
I think there are two valid scientific/philosophical answers without taking religion into it, based on one question:
Are we specifically talking a chicken egg, or the concept of an egg?
In the former case, eggshells contain compounds that cannot exist in nature, and must come from a creature. a chicken egg cannot exist without a chicken before it, thus the chicken came first.
In the latter case, various evolutionary splits happened between animals evolving egg developing capability and some animals evolving into chickens. From this we can say that the egg came before the chicken.
Worst case, this solved exactly nothing. Best case, it can be an exercise in reasoning.
I’ve always interpreted it as which came first, the chicken or the chicken egg?
But I’d just like to point out not all religions have that view of creationism vs evolution, and even within Christianity it’s really only your super conservative, and very loud, fundamentalists. Catholicism doesn’t have an official stance on evolution, iirc, the Episcopal church in the USA is fully supportive of evolution, as are most mainline Christians. Not to detract from your point or anything, I just don’t like seeing all religious people, or all Christians, lumped together with some of the worst examples of religiosity that the US has to offer.
Religion is usually bad, so I don’t have an issue lumping them all together.