Hebrews 2:13; (Isaiah 8:17-18)

And again,
“I will put my trust in him.”
And again,
“Behold, I and the children God has given me.”
(Hebrews 2:13 ESV)

This is a reference to the Messiah speaking, as a man, placing his hope, his only hope in God. Jesus identifies himself with the people--fully man. "I will look to him; I will put my confidence in him." And this relationship Jesus has with His people is the same closeness a father has with his children. They were of one family; one nature. He identifies with man.

Hebrews 2:12; (Psalm 22:22)

saying,
“I will tell of your name to my brothers;
in the midst of the congregation I will sing your praise.”
(Hebrews 2:12 ESV)

This quote from Psalm refers to the Messiah in the psalm. Jesus is declaring that he will make know to his brothers (us) the character of God. He is with them. He is united with his disciples.

Hebrews 2:11

For he who sanctifies and those who are sanctified all have one source. That is why he is not ashamed to call them brothers,

(Hebrews 2:11 ESV)

There is a special union between Jesus and man, so much so that Jesus became a man and took on sufferings of man, and took lowly man and made him holy as He is. We have a oneness with Him. And we are part of His family.

Hebrews 2:10

For it was fitting that he, for whom and by whom all things exist, in bringing many sons to glory, should make the founder of their salvation perfect through suffering.
(Hebrews 2:10 ESV)

Jesus was the perfect fit from God. God, the author and sovereign One, provided a perfect salvation. And this was a plan to save many to heaven. Jesus is not just the one that carries it out, but he is called the founder, the author, the source. Jesus did not become perfect through suffering nor was his exaltation a reward for suffering, but he is complete and fully qualified through suffering.

Hebrews 2:9

But we see him who for a little while was made lower than the angels, namely Jesus, crowned with glory and honor because of the suffering of death, so that by the grace of God he might taste death for everyone.
(Hebrews 2:9 ESV)

The dominion given to man was instead completely fulfilled in Jesus. How could someone who suffered and died be considered higher than angels? His position to man was one of submission and following his death he was immediately crowned with glory and honor and this crowning or exalting was because He suffered. God's grace (His favor, His benevolence) was given for everyone, by Jesus dying, experiencing death, tasting that which is most unpleasant.

Hebrews 2:8

putting everything in subjection under his feet.”
Now in putting everything in subjection to him, he left nothing outside his control. At present, we do not yet see everything in subjection to him.
(Hebrews 2:8 ESV)

Everything has been put under man's leadership.Yet, his dominion over the lower world was temporarily removed when Adam/Eve sinned. Jesus has completely fulfilled this role.

Hebrews 2:7; Psalm 8:5

You made him for a little while lower than the angels;
you have crowned him with glory and honor,
(Hebrews 2:7 ESV)

God made man inferior in rank to the angels, but exalted him almost to their rank. God has bestowed honor on man's nature. Elevated honor conferred on human nature. The author later applies to Jesus. Jesus took exaltation to a greater level.