Sure, but if you’re using the IVT as a proof that there was a point where there was indeed a “first chicken egg”, you still haven’t answered whether the first chicken egg came before the first chicken. Clearly there was a first egg and there was a first chicken, IVT proves this, but which came first? This depends on those definitions. We’d need to find exactly where it “passes over”, which could depend on who you ask.
If you define a chicken as hatching from a chicken egg (“every chicken must have hatched from a chicken egg”), then the egg came first. If you define a chicken egg as an egg that was laid by a chicken (“all chicken eggs must have been laid by chickens”), then the chicken came first. And notice how these definitions are not necessarily mutually exclusive, leading to this whole philosophical issue in the first place.
If, in a much more extremely broad sense, we’re asking which came first, chickens or eggs in general, then I think we could agree that eggs came first, as I believe creatures were laying eggs long before the first “chicken” emerged, for most definitions of “chicken”.