The exodus of the Israelites from Egypt occurred at a precise moment both in terms of the time of the year and in terms of the time of the day.

[A verse describing the exodus from Egypt states:] “He joyously [bakosharot] takes out prisoners” (Psalms 68:7). What is the meaning of bakosharot?… Rabbi Akiva said: He liberated them only during a month fit [kasher] for departure: Not during Tammuz, due to the heat, and not during Tevet, due to the cold; rather, during Nisan, which is fit for setting out on a journey, as there is not severe heat nor severe cold. The Holy One, blessed be He, said: If I take the Israelites out of Egypt at night, the Egyptians will say: Now He acted in the manner of thieves. Rather, I will take them out at midday, when the sun is most powerful, as it is stated: “It was in the midst of that very day, the Lord brought the children of Israel out of the land of Egypt, in their hosts” (Exodus 12:51). (Bemidbar Rabba 3; Pirkei deRabbi Eliezer 48)