How do we know Christ's priesthood is superior?

In Hebrews 8, it is established that Christ is not just a high priest by lineage but the fulfillment of the priestly role, standing at the right hand of God. Unlike the earthly priests who are continually required to offer sacrifices for their own sins and for the people, Christ's singular sacrifice on the cross was sufficient to atone for all of His people's sins forever. He administers a superior ministry in the heavenly places, ensuring that the new covenant, based on better promises, is the ultimate means by which we approach God.