And it shall be, if they do not believe even these two signs , or listen to your voice, that you shall take water from the river and pour it on the dry land. And the water which you take from the river will become blood on the dry land. This sign is not primarily to prove the event, but to validate the messnger who is announcing the event. There is a word play going on this text. In this text the staff is physical object that is to be associated with the doing of the signs.
Staffs form an important part in Egyptian conceptualization of power and authority.
Yahweh is going to be pitting a shepherd and his staff of wood against a Pharaoh and his staff of gold. So Moses told Aaron all the words of the LORD who had sent him, and all the signs which He had commanded him. And Aaron spoke all the words which the LORD had spoken to Moses. Then he did the signs in the sight of the people. Tomorrow this sign shall be.