Perhaps, our cultural take on how one should react to miracles may yield misunderstanding of the Egyptians' reaction to the miracle of Moshe's rescue. I.e. while the Torah does not seem to present the situation as miraculous, our tradition tells us that Mitzrim indeed interpreted events of Moshe's rescue as miraculous and attributed him supernatural powers from that moment on. Moshe survived because he was an unusually big child. Because Moshe did not drown in the Nile river (an object of worship), egyptiansEgyptians felt that he had powers over it. Later Pharaoh considered himself a god and would not speak to Moshe if there was no known supernatural reputation about him, as Shemot 4:16 states literally. Therefore, Torah does indeed present the whole incident as miraculous from its very beginning by noting how egyptians reacted to it.
Finally, we know that daughter of Pharao call the baby Moshe, as the root משה means draw out of water. However, daughter of Pharao could not speak Hebrew, so the question is what does the name mean in Ancient Egyptian language. According to the book "Accuracy of the Bible" by egyptologist Abraham S. Yahuda (section II, chapter 1), the etymology of the name Mosheh is an expression of two words: "mu" - seed, son, child and "sheh" - body of water, pond, lake, specifically applied to water of the Nile river itself. I.e. Mu-sheh - son of the Nile - an Egyptian divine name.