A cursory reading of these verses might give a person the impression that God was just sitting on His throne, twiddling His fingers, and waiting for Israel to do something. But God had already begun to act. He had ensured that Moses would live through the slaughter of the Israelite children. He had directed the little ark into the hands of the Pharaoh's daughter. He had ensured that Moses would receive the benefit of a tremendous education, the best kind of secular education that one could receive at that time. He had put thoughts in Moses' mind that he could be Israel's deliverer. He had spared Moses' life when the Pharaoh tried to take it. He had prompted Moses to flee the land and led him into the wilderness to the family of Jethro. He had given Moses the time and the opportunity to continue his preparation for leading His people out of Egypt.
Who initiated all this? Certainly not the children of Israel! God did! We find all the way back in the book of Genesis that God had already prophesied that in about 400 years, He would move to bring the children of Abraham out of a captivity, which He also arranged.
Could God - who does not change, who sets patterns in His Word so that we will understand - ensure, long before we were born, that there would be a church for His people at the end time and that someone would be prepared by Him to get the doctrines they would need to understand at the end time? We know very well He could - and did.
How did Israel get out of Egypt? Not through any rebellion, revolution, intelligence, or negotiations on their part. They got out because God wanted them out. It was part of His purpose.