It comes down to language no matter how you look at it. Nothing we describe with discrete words is actually discrete. If you think of evolution, it comes down to: when did the bird the chicken evolved from become a chicken? Was there a first chicken, born of not-a-chicken? Where do you draw the line between "chicken" and "not a chicken"? Only when you find that line can you decide "the first chicken came out of an egg not laid by a chicken/not a chicken egg, therefore the first chicken came before the first chicken egg" or "A not-a-chicken laid the first chicken egg, aka the egg from which the first chicken hatched". Which again is just another, long and roundabout way of saying it depends on if you define the egg by what laid it or what it contains, like you said.

So, "Which came first, the chicken or the egg?" boils down to just an older form of "is a hotdog a sandwich?"

Language requires words, and we treat the words like they have specific meanings to one degree or another because otherwise we couldn't communicate, but reality isn't beholden to the structure of our language, or to the structure of the way our brains evolved to divvy concepts up into boxes. Sometimes big boxes, sometimes little boxes, but still boxes that don't perfectly match reality.

Tldr questions like this don't have any true answer because the premise that there is a real, sharp border between the concept of a chicken and the concept of not-a-chicken-yet, or between the concept of a sandwich and the concept of a hotdog, is false. They can be fun to argue about, with everyone proposing different but equally arbitrary differences between the two concepts, but ultimately it's just a linguistic amusement.

Sidenote: the chicken vs not-a-chicken-yet conundrum crops up in taxonomic classification all the time, too, even across present day species. I remember reading a Stephen J. Gould essay ages ago about some lizards; some lived on one side of a mountain range, and others lived on the other side, so the populations were somewhat separated by the terrain and didn't intermix evenly over time.

On the far end of one side of that range, there is lizard Species A (let's call it), and on the far side of the end of the range, there is Species B, and Species A and B are obviously different and cannot mate and produce viable offspring, so they're clearly different species. Except, if you start at Species A's end of the range and start looking at the lizards between them and Species B's end, you find a steady spectrum of lizards that look phenotypically and genetically less and less like Species A and more and more like Species B, and which can still breed with each other and produce viable offspring, until at some point you reach Species B. So what do you do, if you're trying to put animals into species boxes? Even though A is clearly different from B, there's all these lizards in the middle that don't fit either box. And cutting them off into a separate Species C wouldn't make sense either because then you'd still have a species of which some members can breed only with Species C and Species A, but of which others can only breed with Species C and Species B, plus having other differing traits.

You have to pick a place to draw a line to be able to talk about the differences between Species A and B, but that line is always quite arbitrary and artificial no matter where you put it.

Tldr language and everything about the way we use it to describe the world is a social construct, more at 11.