Short answer
No. Greek science did exist in the region, but none of it was in Arabic in the lifetime of the Prophet Muhammad (ﷺ). It was in Greek and Syriac books, and in Persia. Syriac, a form of Aramaic, was the written language of Syria's Christians. The Arabic translations of Galen and Aristotle were made in Baghdad, more than a century after his death. He could not read, and Mecca had no school of Greek learning. The strongest answer is the mistakes. Anyone who learned Greek science learned its errors with it: a womb with two horns, a child fed on menstrual blood, lightning as burning vapour. A copier takes his source's mistakes. The Qur'an speaks on the same subjects and repeats none of them. It avoids the Bible's errors too, though critics say the Bible was its source. Islam teaches that the Qur'an came from God (﷾).
Full explanation
Where Greek learning was in the seventh century
Mecca was a caravan town trading with Syria, Yemen, Abyssinia and Persia. Greek medicine and philosophy were read in the region, but in Greek and Syriac. They were read in the monasteries of Syria, and in Persia, where later Arabic writers remembered Jundishapur as a centre of medicine. Nothing of it was in Arabic. Historians date the translation of Greek science into Arabic to Baghdad under the Abbasid caliphs, from the second half of the eighth century. That is more than a century after the Prophet (ﷺ) died in 632.
The standard history of the Graeco-Arabic translation movement. It shows that the translation of Greek science and philosophy into Arabic was an Abbasid project centred on Baghdad, running from the second half of the eighth century to the tenth, with Greek works earlier available in the region mainly in Syriac.
The best-known Arab physician of the time
Al-Harith ibn Kalada of Ta'if is the best-known Arab physician in the time of the Prophet (ﷺ). A thirteenth-century history of physicians reports that he learned medicine in Persia. No known report has him teaching the Prophet (ﷺ) anything, about the embryo or anything else.
A thirteenth-century history of physicians. Its chapter on the physicians of the Arabs names several of the Prophet's (ﷺ) time, among them Ibn Abi Rimtha al-Tamimi and al-Nadr ibn al-Harith. Its entry on al-Harith ibn Kalada of Ta'if, the best known of them, reports that he travelled and learned medicine in Persia. It does not describe him teaching the Prophet.
A man who could not read
The Qur'an reminds its first hearers that the Prophet (ﷺ) had not recited any book before it, and could not write one out. His opponents did accuse him of having a teacher. The Qur'an answered in his lifetime. The man they pointed to spoke a foreign tongue, and the Qur'an is clear Arabic.
“And thou wast not (able) to recite a Book before this (Book came), nor art thou (able) to transcribe it with thy right hand: In that case, indeed, would the talkers of vanities have doubted.”
“We know indeed that they say, "It is a man that teaches him." The tongue of him they wickedly point to is notably foreign, while this is Arabic, pure and clear.”
A copier takes the mistakes too
Grant, for argument's sake, that a well-travelled Arab heard in the market that a child grows in stages. He would have heard the rest of the teaching too. Galen described a womb with two horns. Greek medicine fed the child on menstrual blood, put boys on the right side, and held that a child born in the eighth month dies. Aristotle explained thunder and lightning as a dry vapour striking the clouds and catching fire. And the Bible, which critics say was the Qur'an's source, sets the earth on pillars and has plants growing before the sun. Even a short summary of the Greek teaching on the child, heard by word of mouth, would carry its core. That core is that the child is made from, and fed on, menstrual blood.
Galen's short anatomy of the womb, drawn largely from the dissection of animals, which describes the human uterus as having two horns.
A history of embryology from antiquity to the eighteenth century. It sets out the Greek and Galenic teaching that the embryo is formed from and nourished by the mother's menstrual blood, and the ancient view that males develop on the right side of the womb and females on the left.
A treatise in the Hippocratic collection holding that a child born in the seventh month can live but a child born in the eighth month cannot. The belief passed into later Greek medicine.
Aristotle teaches that the sun draws two exhalations from the earth: a moist one, vapour, and a dry, smoke-like one (Book I, ch. 4). In Book II, ch. 9 he explains thunder as the dry exhalation, trapped in a cloud and forced out, striking the surrounding clouds, and lightning as that same ejected exhalation burning with a fine, faint fire.
“for the pillars of the earth are the Lord’s, and he hath set the world upon them.”
“Which shaketh the earth out of her place, and the pillars thereof tremble.”
“And God said, Let the earth bring forth grass, the herb yielding seed, and the fruit tree yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so. And the earth brought forth grass, and herb yielding seed after his kind, and the tree yielding fruit, whose seed was in itself, after his kind: and God saw that it was good. And the evening and the morning were the third day.”
“And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years: And let them be for lights in the firmament of the heaven to give light upon the earth: and it was so. And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also. And God set them in the firmament of the heaven to give light upon the earth, And to rule over the day and over the night, and to divide the light from the darkness: and God saw that it was good. And the evening and the morning were the fourth day.”
What the Qur'an says instead
On the same subjects the Qur'an says a few plain things and stops. The child comes from a mingled drop and is formed in stages. There is no two-horned womb, no menstrual blood and no eighth-month child. The storm cloud is driven, joined and heaped up, with hail and blinding lightning, and there is no burning vapour. None of these learned errors appears. Critics point to 86:6-7, on where semen comes from; it has its own page. The Prophet (ﷺ) could not read those sources. And even a man who could read them would not have known which parts were true and which were errors. That took the best part of a thousand years of later science.
“Verily We created Man from a drop of mingled sperm, in order to try him: So We gave him (the gifts), of Hearing and Sight.”
“Man We did create from a quintessence (of clay); Then We placed him as (a drop of) sperm in a place of rest, firmly fixed; Then We made the sperm into a clot of congealed blood; then of that clot We made a (foetus) lump; then we made out of that lump bones and clothed the bones with flesh; then we developed out of it another creature. So blessed be Allah, the best to create!”
“Seest thou not that Allah makes the clouds move gently, then joins them together, then makes them into a heap? - then wilt thou see rain issue forth from their midst. And He sends down from the sky mountain masses (of clouds) wherein is hail: He strikes therewith whom He pleases and He turns it away from whom He pleases, the vivid flash of His lightning well-nigh blinds the sight.”
“He is created from a drop emitted- Proceeding from between the backbone and the ribs:”
Perspectives
The Islamic perspective
The Prophet (ﷺ) did not learn the Qur'an from Greek or Persian science. That learning was not in Arabic, and he could not read. The Qur'an also lacks the errors any copier would have carried over.
Greek scientific works were translated into Arabic in Abbasid Baghdad from the second half of the eighth century. That was over a century after the death of the Prophet (ﷺ).
The Qur'an states that the Prophet (ﷺ) had not recited any book before it and could not write one.
The charge that a man taught him was raised in his lifetime. The Qur'an answered that the man's tongue was foreign while the Qur'an is clear Arabic.
The reports about the physician al-Harith ibn Kalada say nothing of him teaching the Prophet (ﷺ).
The learned sources of the age taught a two-horned womb, nourishment by menstrual blood, and lightning as a burning exhalation (vapour). The Qur'an repeats none of these.
A copier carries over his sources' mistakes. So a text on the same subjects with the truths and none of the mistakes did not come from those sources.