Natural priesthood
But I suffer not a woman to teach, nor to usurp authority over the man, but to be in silence. For Adam was first formed, then Eve. And Adam was not deceived, but the woman being deceived was in the transgression. Notwithstanding she shall be saved in childbearing, if they continue in faith and charity and holiness with sobriety. (1 Timothy 2:12-15)
If the relationship between Adam and Eve provides a paradigm for the Levitical priesthood and for the church's pastoral ministry, it would seem to follow that the prelapsarian created order had some kind of natural priesthood.
This is another way of saying that the priesthood was not a postlapsarian institution, introduced fundamentally to deal with sin, but was rather an ordinance embedded by God into the order of nature itself. More fundamental than its remedial function of dealing with sin is its liturgical function: to lead the rest of the creation in worship. In his redemptive work, God does not abolish the created order but restores and perfects it. So it is fitting that God's redemption of the world takes effect by establishing Christ as a great high priest, and his church as a holy priesthood.
As the church appoints men to be its elders and pastor-teachers, and as women persevere in childbearing and managing their households, the church learns to live in terms of reality, and in that way God is restoring the natural order. A church that lives faithfully in terms of the natural order is a blessing to its unbelieving neighbours, whether or not those neighbours appreciate or understand what they are seeing. We are showing them that heavens and the earth are going to arrive at their proper end under the great high priest Christ, which is wholehearted praise of its wise and kind creator.