Every Jewish woman has the power to make Jewish souls before giving birth. This has been the Orthodox Jewish view in the past, and remains the Halakah for all Orthodox Jews to this very day.
Abraham did not have this power. Abraham was the first Jew but he did not have a Jewish mother or a Jewish father. Since there were no other Jews to make him Jewish Abraham must have mit-ya-haid (see Book of Esther (9:17 & 27) self converted; but he and all his male descendants could not make any fetus Jewish pre birth.
However Sarah, her daughters, and all non-Jewish women like Ruth, who desire to join the Jewish People and have Jewish children, have the power to make Jewish souls pre-birth.
The only reason for this amazing power of Jewish women offered by Orthodox male Rabbis is the mundane fact that everyone knows who the mother is, but who the father is, is subject to doubt.
I think we need more spiritually elevated explanations. For example one of the Biblical names for God is El Shadai. I believe when pregnant Jewish women pray to El Shadai (the God of the breast) and the Shekinah for a healthy birth; and a successful breast nursing experience, they felt and become more personally and spiritually healthy.
Given the world wide very high rates of maternal and infant deaths that were normal worldwide until the late 19th century; one can feel the relief they felt when their prayers were answered.
This practice probably goes back to the beginning of Homo Sapiens religious consciousness because the intelligent minds of Homo Sapiens knew the dangers of childbirth. Infant mortality rates in most tribes were more than one in four and the maternal death rate for every four births was more than one in ten.
Pregnancy was highly desired and birth anxiously awaited. Pregnant women naturally sought the physical help of their mothers and grandmothers who in turn sought the spiritual help of their now departed mothers and grandmothers.
Among the earliest Gods were birth Goddesses. Small stone figures of very pregnant birth Goddesses, often referred to as “Venus” figures, go back 30-35,000 years. They are the first examples of iconic religion. The worship of spirits within natural phenomena does not need iconic representation. But birth and nursing rarely took place in the open or in public.
The birth Goddess needed to be present in some tangible way in order to ease the anxiety of women in labor. Even today in some African countries the maternal mortality rate is 3% per birth. A woman who gave birth to 8 children had a one in four chance of dying from giving birth.
Any Homo Sapiens band would benefit even if the presence of Goddesses reduced that mortality rate by only 5%. Carvings in wood of birth Goddesses probably preceded stone statues by many millennia and may have originated 40-70,000 years ago.
Infant mortality during the first 2-3 years was 30-40%. After that it dropped to almost current rates. With the development of clay ceramics in the last 10-15,000 years one could make an image that would be used from the time when the belly swelled until nursing ended.
The Torah tells us that not until the generation of the Exodus was the one God YHVH known as the lawgiver of sacred scripture. “I am YHVH. I appeared to Abraham, Isaac and Jacob as El Shaddai but I did not let myself be known to them by my name YHVH.” (Exodus 6:3)
El Shadai is the God of the breast or the chest. This signifies the divine spirit within each individual, and/or the maternal nurturing mystical soul that is invoked in most Indian and some East Asian religions; the mystical religions of inner enlightenment and personal rebirth or escape from the corruption of the material world. This was an advance for women beyond just invoking spirits and the hierarchy of sky Gods or some remote high God.
The God of Breasts/El Shadai was still very important for pregnant and nursing Jewish mothers until the era of the First Temple, when the name El Shadai stopped being used in the Hebrew Bible, although it still remained in use on most Mizuzot.
In more modern terms: Got hot nit gekent zayn umetum, hot er beshafn mames. “God couldn’t be everywhere, so He created mothers.” And: Ein mama dergreykht mer vi a hundert lerers. “One mother achieves more than a hundred teachers.”