No, it wouldn't make sense. The answer is in the question itself. Legally, a person is considered a person from the moment of the first breath, that is, from the moment of birth. Before that, it is not a person, but an embryo. In addition, as already correctly noted, it is not always possible to accurately determine the moment of conception. And most importantly, why?
It seems to me that it is not always possible to accurately establish the moment of embryo formation. And also not every embryo will reach birth (for example, abortion).
Judging by Wikipedia: Embryo (ancient Greek ἔμβρυον), an embryo is an early stage of development of an animal and a person, starting from a fertilized egg (zygote ). And, for example: Identical twins (homozygous, identical or monozygous) are the result of multiple pregnancies resulting from the fertilization of one egg and the development of two or more fetuses (twins). That is, at first the cell was fertilized (embryo), and then divided into two. It would also be an interesting situation)
Considering that women do not give birth like clockwork, and the gestation period is always slightly different, it is difficult to say from what moment the age should really be considered. In addition, age is just a legal formality and it is easier to tie it to a clear date than to something abstract. However, counting age from the moment of birth is not practiced everywhere. So in Korea, since ancient times, it is customary to count the age of a person not from the moment of his birth, but from the beginning of the year when he was born, as if rounding off the time while the child was in the womb.
I will make an assumption from a purely medical point of view. And how to reliably, with an accuracy of the day, hour and minute, establish the reliable moment of embryo formation? This is actually impossible yet.
With the birth, everything is simple.