Chapter 1 starts out telling how the people of Israel(Jacob's descendants) were fruitful and multiplied into a very large group in Egypt. This goes with God's command in Genesis and promise He gave Abraham, Isaac & Jacob.
The Israelites had been living peacefully. However, a new king came to power, that wasn't informed of the past and how Joesph saved Egypt, so he only saw a large group and feared that they would try to take over. Because of that fear he enslaved the people and when that wasn't enough he ordered all the sons born to be killed.
The midwives Shiphrah and Puah I would say must have either seen God do something or heard the stories of the past that they feared Him more than the Pharaoh. They lied and disobeyed the Pharaoh's order, which God blessed them for doing by giving them families. On a side note, I find it interesting that the writer names the midwives but doesn't bother to say the Pharaoh's name.
Moses's parents were Levites, which is the tribe that the priests come from later on.
All sons born were to be thrown into the Nile. Moses's mom hid him for 3 months before she ended up putting him in a basket into the Nile. Knowing from personal experience with babies that she was able to hid him for 3 months is pretty impressive.
I love how of all the people that could have found him God had Pharaoh's daughter find him. Then unknowingly she ends up paying his own mom to nurse him. Talk about God making a way.
I believe there is significance in the fact God uses certain numbers/amounts of time repeatedly. From research I have found that people say that the number 40 is in the Bible 146 or 159 times. I didn't count myself, I might do it another day. The consensus though is that the number 40 is normally but not always associated with tests, trials, probation or judgment.
At age 40 Moses despite being raised as an Egyptian obviously knows he is Hebrew and stands up for a Hebrew that is being beaten. Moses ends up killing the Egyptian. God saves Moses life by having him flee.
40 years later God hears the cry of His people and remembers the covenant He made with Abraham, with Isaac, and with Jacob. When God says He remembers something it doesn't mean He had forgotten about it, it means that He is about to take action.
Final notes for chapter 2 I found interesting. First is the fact that Moses ends up meeting his future wife at a well. A well was also involved with Isaac and Jacob finding their wives. I wonder if part of it is because a well is water and that symbolized life. Also I think it's significant that Moses's wife was the daughter of a priest.