The Lord has said to Me, “You are My Son, today I have begotten You.” Psalms 2:7

I know this scripture but not from the Psalms. I recall it from Hebrews 1:5 where the writer compares the angels and the Son. The writer of Hebrews plucked this single phrase from Psalm 2 as his argument on the lowliness and superiority of Christ.

Although King David wrote a great portion of the Psalms, much of it is spiritualized as the words of Jesus, like Psalm 22 where the crucifixion is clearly seen and, indeed, Jesus spoke the leading words from the cross.
Jesus also used the Psalms in His teachings.

I’m sure David felt like a son of God, blessed with the responsibility of the kingdom of Israel. He was king. He was ruler. He was the Godly example of his people.
Like a son, David received the inheritance of Israel.

I can say that my Lord has said the same thing to me – You are my son, today I have begotten you!
How can I make such a claim?
The same way you can.
Gal 3:26 For you are all sons of God through faith in Christ Jesus.