Not a chicken -> egg -> not a chicken -> egg -> chicken!
Not a chicken -> egg -> not a chicken -> egg -> chicken!
We have a few such cases without needing to use time travel. We often refer to them as ring species, but a single ring species would become multiple species if you had one or two areas of the ring wiped out (based on if it is really an unbroken ring or an arc). That the death of one group of animals turns two other groups of animals from being one species into two shows the underlying problem with our classification system.
My original statement was simplified, maybe "evolution in conjunction with how mankind classifies species" would be more in line with the point I was making. My reasoning behind this is the following: As far as I know, the most accurate way of comparing species is by comparing genetic structure. And the point at which these genetic changes typically happen (maybe there are exceptions) is at reproduction (that's the evolution aspect of my point). This would also be the "earliest" point we could spot a difference.