I have enumerated the parts of the human soul as follows:
Living, vegetative, sensitive, self-moving, and rational. It's a Tower of Hanoi sort of setup, whereby each more sophisticated part of soul rests upon all the more primitive ones.
Lower creatures have some but not all of these. There are several possibilities.
First, a full-featured soul may be created by God or descend from heaven immediately upon conception. The body's stage of development determines how severely the soul is handicapped in its powers. This opinion has problems. For one, if a miscarriage occurs sufficiently early during gestation, a frequent enough affair, then the soul would have to go back to heaven empty-handed, or without useful experiences, in vain. The idea of such objectionably masturbatory trips back and forth seems sufficiently comical not to be taken seriously. In addition, this makes especially embarrassing the problem of the "limbo" of the children in Christian theological speculation (which admitting reincarnation may of course render irrelevant) being populated mostly by embryos.
The second possibility is that God uploads each faculty into the body as it gestates step by step. This, too, is unsatisfactory. Now the fertilized egg is alive and so has a living soul at the outset. If all further faculties, vegetative, sensitive, etc., are forged and infused by God, then God would also have to control the prenatal growth of all plants and animals. A plant produces a seed, and suddenly God has to supervise the seed's "spiritual" development. Two porcupines have sex, and God immediately has to concern himself with their offspring, timing their soul developments perfectly. And this is absurd.
Third, perhaps the entire soul of any creature develops naturally, including through the stages described, along with the body. This has some attraction, but still is rather iffy, because the rational faculty is far too mighty a power simply to up and arise. One and one's soul either are rational or not; the gulf between the two is unbridgeable. And there is another major difference in kind: a rational soul is naturally immortal (once it exists) and is slated for heaven, while a non-rational soul is naturally corruptible and is indeed like a "puff of smoke that appears briefly and then disappears."
In addition, this solution is incompatible with reincarnation; hence, it depends on the fairly controversial premise that reincarnation is not a thing.
Therefore, we must assert that the vegetative, sensitive, and self-moving spiritual human faculties develop on their own accord along with the body of the embryo / fetus, while the rational faculty is either created by God or comes down from heaven, snapping securely into place in the fullness of time. The rational part completes the human soul's development as though a crown were placed on the king's head. (Again, this does not entail that the fetus can now think; rather, it would be able to think but for the primitiveness of the body which at this point shuts off most of the soul's powers.)
For example, only a few days after fertilization, cellular differentiation begins, thus endowing the embryo with the dignity of a plant and its vegetative "growing" soul. Unlike the conferring of the rational soul, this seems to require no divine action.
The benefits of this understanding are many.
First, it neither precludes nor requires reincarnation.
Second, it postpones the creation of the rational faculty considerably, into the 2nd trimester, thus preventing numerous apparently superfluous and frustrating journeys of a soul from heaven to earth and back; even without admitting reincarnation, it makes somewhat less offensive the ugly artifice of the limbo. Before its acquisition of the rational soul, the embryo's soul is not at all immortal and simply corrupts if the embryo dies, e.g., it is somehow absorbed into God or dissipated with no consequences.
Third, it suggests reasonably that early abortions are not immoral, with 21 weeks at quickening being the upper limit on permissible abortion. The correct cutoff age could of course be even earlier; thus, Wikipedia informs us that during weeks 13 to 16, "the fetus makes active movements; sucking motions are made with the mouth"; and even during weeks 10 to 12, "the fetus can make a fist with its fingers." It appears that the power of self-motion develops fairly early during pregnancy, at which point the rational soul can be finally infused. Once the soul is completed, aborting the unborn child is a major sin.