At what moment after conception if any would you say that the soul entered the body, and how would you define that astrologically in the chart?
The kind of question I like since it gives me an opening to break up the kinds of boxes that start boxing in thinking even within astrology. I've read The Arkana Dictionary of Astrologery by Fred Gettings virtually cover-to-cover. I find the abstract metaphysical speculation by Bailey, other esotericists and the Theosophists to have no practical value within the field of astrology or in answering real questions. These questions relating to the process of incarnation are not answered or served at all, in my opinion, with answers entangled with the limitations and abstractions of astrological language.
So I will answer your question directly, based on my understanding of the Edgar Cayce readings on the topic, and on the accounts of NDE survivors who have been there and returned, and based on my own dynamic relationship with the "other side" from which we come.
The Soul is to be understood differently from Spirit. Soul is an individuation of Spirit, but "spirit" also refers to the very life force itself that every Soul has as its own. So when a Soul incarnates, it extends its life force (etheric silver/blue cord) to the human body to begin the process of living as a human. This moment is THE birth moment and happens most often (up to 4 hours or more)
before physical birth, but can happen shortly thereafter. Cayce called this "spiritual birth" (I personally don't like the term, but it appears necessary to understand the overall process). The moment when the full embodiment happens is termed "soul birth" and generally happens after spiritual birth.
The silver/blue etheric cord that NDE survivors say they see connecting them to their bodies while they are being worked on in the ER or operating room is that Spirit referred to by Cayce's description of spiritual birth. Death does not actually take place until that cord has been severed or pulled from the body. As long as it is connected to the human body that is that person, it is still alive (even if not by medical/scientific definition). Life is defined spiritually, not materially only.
Astrologically, there has to be a particular relationship (of which I am uninformed) between Sun, Moon, Uranus, Ascendant for ANY incarnation to occur. While a body can pop out of a mother's womb at any time (the mother's biological finishing process), an interdimensional opening must take place (Sun-Moon-Uranus-Asc) for the real entry to happen.
You have to remember that an interdimensional event is taking place that cannot be described in the terms of ordinary mundane consciousness. Nor do the metaphysical (or even astrological) abstractions of esotericists help much in understanding this process. Most of it is nonsense in my opinion. Instead
read the accounts of NDE experiencers and know that they are experiencing birth in reverse. These accounts come from real people living today and in recent times who can relate it to us in ordinary language without metaphysical abstractions.
A baby-to-be hovers around the prospective mother/father and actually mixes and interacts with their energy layers. I've participated in this process as a prospective father just these last few months (late last year). There is a communicative process that can happen consciously if you choose. It can also occur in dreams. However, charts cast for "conception" are not the charts to use for individuals who have been born since the Soul that may be born to that mother can still change. One may back out and another may step in because it isn't an do/don't kind of thing, so long as the mother still wants a child. Some people even back out last minute, and there is no time left for another soul to take its place, therefore a miscarriage/stillbirth, etc occurs.
It is a fascinating area of study and should be studied increasingly by those who want to master astrology.
I can tell you without reservation that the so-called "first breath" theory does not give consistently reliable natal chart results. It isn't that it is "wrong," as much as it was made by those who were only viewing "birth" through linear eyes boxed in by matter, speculating metaphysically instead of getting information from real experience. We have Near Death Experiencers now who can tell us what they experienced in death, a kind of birth in reverse.
To go from this dimension to the next, a doorway must be opened. It cannot occur just anytime. The "first breath" theory does not take this into account.