Melchizedek was the first priest, king of peace, and had no ancestry, just like Jesus.
Abram paid tithes to him, so he was greater than Levi, a descendant of Abram.
The Levitical priesthood and ritual law do not perfect us, but Jesus does.
Melchizedek shows us that an effective priest doesn't depend on his ancestry, but on the life God gives Him, just like with Jesus.
So it's a better priesthood with a better oath (Psalm 110:4). Jesus never dies, but earthly priests do.
His sacrifice was better. It wasn't needed for His own sins - there were none. It doesn't have to be repeated daily - it's done!
How this is about Jesus
He is a better priest than any we find in the history of the world.
Being from a non-priestly tribe shouldn't slow us down in accepting Him, for God showed in several ways that He was from God, on God's mission, and accomplished it.
Keep yourself from falling back into reliance on whatever it is you used to rely on before trusting Jesus Christ, by focusing on the truth of who He is and what He has done. It's better than anything else you are tempted to trust.