This is where a Levite couple have a child and hide him from the Pharaoh so he doesn’t kill him. When they can’t hide him any more they float him down stream, where he’s found by the daughter of the Pharaoh, she takes pity on him and by some coincidence asks the childs mother to nurse him. It is some time later that she decides to name him Moses, but only after some time has passed, and she apparently didn’t had seen him since. That’s when she named him Moses.
So, Moses grew up and saw other Hebrews are working and killed an Egyptian who was hurting one of them. Because of this he had to flee Egypt to Midian. In Midian he helped some girls trying to water their sheep and their priest father invited Moses to stay with them. Reuel, the priest gave Moses one of his daughters, Zipporah, who then had a son, Gershon,
During that long time while Moses was away the Egyptian King died and the Hebrews cried out because of the slavery. God heard them and was concerned.
So, of course it’s super convenient that Moses’ mother is the wet nurse chosen by the Pharaoh’s daughter.
And it seems we have a case of murder that will go unpunished. We can assume that Moses knows that he is a Hebrew since he saved the slave from the beating and wanted to intervene in the fight between 2 other Hebrews (Exo 2:13).
And lastly, God finally notices that his people are enslaved. This is troubling, because they did nothing to deserve it. They were living peacefully with the Egyptians up until a new Pharaoh decided to enslave them. Go clearly doesn’t pay much attention to his chosen people. It’s only until they are groaning under the oppressions, possibly generations later, that he decides to do even care, let alone do anything about it.