Baptism, all are called to enter a worldwide and even cosmic community. It is vital for us to understand that those who become priests never leave this community, even after their consecration.
Although God calls His people to be a "kingdom of priests," "a holy nation," we realize soon enough in the book of Exodus that this people of God failed in carrying on this priestly vocation. Although many people believe that priesthood began with the tribe of Levites, mainly the clan of Aaron, a careful reading of the Bible shows us that the Levites were only a substitute for a priesthood that existed even earlier.
This summary can be found in the same book of Exodus chapter 32, where we find Moses on the mountain for 40 days. While he delayed in returning, the people who were called to be a "kingdom of priests," and "a holy nation" began to worship the golden calf. When Moses came down and asked his people who was on the side of the Lord, those who were to be "a kingdom of priests" and "a holy nation" were silent, and the Levites came forward. Moses told them, "Today you have won yourselves investiture as priests of Yahweh at the cost, one of his son, another of his brother; and so he grants you a blessing today" (Jerusalem Bible translation).