He was found by Bisyoh the daughter of Paroh who attempted to have him nurse from an Egyptian wet-nurse. Moshe refused, as since his holy mouth would eventually communicate directly with Hashem, he would only nurse from a bas Yisroel. This occurred on the 6th of Sivan, three months after his birth. We likewise consume kosher dairy products on that date. The Sefer Matamim says that upon accepting the Torah, the bnei Yisroel had a status of a newborn person.
Newborn babies feed exclusively on milk.
Rabbi Pinchos of Koritz says that milk is symbolic of humbleness. On the day of the receiving of the Torah we eat humble food to indicate that we receive the Torah while acting humbly. Until Matan Torah milk from a live animal was prohibited. We see from here that a ben Noach was permitted to consume dairy products even before the Torah was given. A possible answer is that he served them dairy products that were taken from a dead animal.