Who anointed the Messiah?

Christians who think that the Messiah is "God the Son" would often bring up two well known verses from the NT.

John 20:28 NKJV
And Thomas answered and said to Him, “My Lord and my God!”

Hebrews 1:8 (quoting Psalm 45:6) NKJV
But to the Son He says: “Your throne, O God, is forever and ever;
A scepter of righteousness is the scepter of Your kingdom.

In contrast, I would like to draw attention to two less frequently quoted verses which gives the bigger picture:

John 20:17 NKJV
Jesus said to her, “Do not cling to Me, for I have not yet ascended to My Father; but go to My brethren and say to them, ‘I am ascending to My Father and your Father, and to My God and your God.’”

Hebrews 1: 9 (Psalm 45:7) NKJV
You have loved righteousness and hated lawlessness;
Therefore God, Your God, has anointed You
With the oil of gladness more than Your companions.

Christ means "the Anointed One". Who anointed him?