Thank you for the historicity question, “Do you agree it was God’s power that literally destroyed Pharaoh and the Egyptian army in the Red Sea, according to Psalm 136:15?”
The biblical narrative of the Exodus with its dating of 1446hu BCE or 1290 BCE is contested by archaeologists due to the limited archaeological discoveries.
If one accepts the biblical narrative, and I do, then Psalm 136 is an accurate recounting of creation of the world to the conquest of the Promised Land. Psalm 136:15 expresses the means whereby God delivered the Israelites from Egypt and led them into the Promised Land.
With the Thutmose III being Pharaoh, it may have been here that Moses was born. “Thutmose III was the son of Thutmose II; his mother was one of the king’s secondary wives or a lesser harem queen, named Isis. Since there was no prince with a better claim to the throne, the boy was crowned king on the early death of his father; he was very young at the time.
Hatshepsut—the daughter of Thutmose I, the wife and sister of Thutmose II, and the mother of Thutmose III’s half-sister Neferure—acted as regent. By the seventh year of his reign this strong-minded and ambitious woman herself assumed the attributes, dress, and insignia of a king and to all intents and purposes reigned in his stead. As one of her courtiers says, “she directed the affairs of the whole land according to her wishes.” Still, Thutmose was given an education befitting his royal station. He was taught all military skills, especially archery, which he demonstrated in public display, and horsemanship, in which he showed considerable prowess. He was later to boast that none among his followers could equal him in physical strength and in marksmanship.
As he grew up, Thutmose may even have been entrusted with command of the army on campaign in Nubia; he may have also fought in Gezer in Palestine. His grandfather Thutmose I had penetrated into northern Syria; Thutmose II, though far from a weakling, had not followed this success, and Hatshepsut may have been unwilling to send an army into the field. Thus, through inaction, Egyptian influence in Syria and Palestine declined. The sons and grandsons of the Syrian princes who had surrendered to Thutmose I no longer sent tribute, and the king of Mitanni, a powerful Mesopotamian kingdom with its capital beyond the Euphrates, was able to extend his control westward to the Mediterranean”
https://www.britannica.com/biography/Thutmose-III
Can it be that during this time period Egypt faced some kind of decline with the loss of their firstborn sons and army? The ascension of a Thutmose III’s lesser son, Amenhotep, fits the narrative of Thutmose losing his first born son leading to the co-regent of Hatshephat.
“Amenhotep appears to have been crowned while still a child, perhaps between the ages of 6 and 12. It is likely that a regent acted for him if he was made pharaoh at that early age. He married Tiye two years later and she lived twelve years after his death. His lengthy reign was a period of unprecedented prosperity and artistic splendour, when Egypt reached the peak of her artistic and international power. Proof of this is shown by the diplomatic correspondence from the rulers of Assyria, Mitanni, Babylon, and Hatti which is preserved in the archive of Amarna Letters; these letters document frequent requests by these rulers for gold and numerous other gifts from the pharaoh. The letters cover the period from Year 30 of Amenhotep III until at least the end of Akhenaten‘s reign. In one famous correspondence—Amarna letter EA 4—Amenhotep III is quoted by the Babylonian king Kadashman-Enlil I in firmly rejecting the latter’s entreaty to marry one of this pharaoh’s daughters.
The pharaoh’s reign was relatively peaceful and uneventful. The only recorded military activity by the king is commemorated by three rock-carved stelae from his fifth year found near Aswan and Saï (island) in Nubia. The official account of Amenhotep III’s military victory emphasizes his martial prowess with the typical hyperbole used by all pharaohs.”
https://en.wikipedia.org/wiki/Amenhotep_III
Amenhotep appears to be the son who inherited a powerful and stable nation. Under the co-regency the Egyptian kingdom was able to rebuild their military. It is also interesting to note that he is the Pharaoh who believed in a monotheistic deity or elevated his deity to be the supreme deity. Did this had anything to do with Moses and Pharaoh’s contest in Exodus? It is unclear. It is clear that after his death, the Egyptians returned to the polytheistic deities.
If the Exodus is accurate, the military power of Egypt could have easily defeated the Israelites as their backs were toward the Reed Sea. They were trapped.
If the biblical account is inaccurate that they never left Egypt or a small tribe left Egypt, that the biblical account is exaggerated or untrue, the very foundation of calling for truthfulness of not bearing false witness in the Ten Commandments would be violated by the writer or copyists. It follows that if the Exodus never happened, then there is no Mount Sinai or the Tabernacle.
The nation of Israel based their history with the first Passover. This dating has been accepted through the centuries. Although there are scant evidences of the Exodus, the continual archaeological digging in Israel may or may not confirm the Exodus. Additionally one must remember that the Jews did not build any settlement in their wandering for 40 years and their conquest of the Promised Land soon led them into idolatry after one generation.
SUMMARY: The command of truthfulness in the Ten Commandments requires the Israelites to accurately record their history.