According to Evangelicalism when did Jesus become the High Priest?
Well, Hebrews has a lot to say about this, but I'll narrow the scripture references down to just a few that most clearly indicate when Jesus became a priest.
1. After he had become human.
14 Since therefore the children share in flesh and blood, he himself likewise partook of the same things,...
While I don’t think we can pinpoint the exact moment when God declared Jesus our High Priest, I believe the Book of Hebrews gives us an idea of a general time period.
Hebrews 7:20-21 tells us that Jesus was made our high priest by an oath sworn by God the Father.
Hebrews 7:20-21 (KJV):
20 And inasmuch as not without an oath he (Jesus) was made priest: