You explain in the question, “What does the Bible mean when it says Jesus is the only begotten Son?” that the expression “Son of God” meant that Jesus was and is God. Then how do you explain “begotten” (Greek gennao) in the quotations of Psalm 2:7 in Acts 13:33, Hebrews 1:5, 5:5? since this verse is quoted three times. It must be important.
The question you are referring to can be found here. It is important to note that the phrase “only begotten” in John 3:16 is not the same Greek word that appears in Acts 13:3; Hebrews 1:5 or 5:5. The phrase “only begotten” comes from the Greek word monogenes which means that Jesus is the unique or “one and only” Son. monogenes occurs only five times in the New Testament: John 1:14; 3:16, 18; Hebrews 11:17 and 1 John 4:9. In a question titled “Why was Jesus called the ‘Son of God’?” we discover that the phrase “Son of God” is defined by Jesus and it means “God.”
When we come to the word “begotten” in Psalm 2:7, we enter into a different arena of meaning. Here is Psalm 2:7,
I will surely tell of the decree of the LORD:
He said to Me, “You are My Son,
Today I have begotten You.” Psalm 2:7 (NASB)
As you have indicated, this Old Testament passage is quoted in Acts 13:33; Hebrews 1:5 and 5:5.
The Hebrew for “begotten” is yalad and the lexical meaning is “to bear, beget, or bring forth.” The three New Testament passages help us understand how it should be understood in Psalm 2. For example, in Acts 13:30-34 we read,
But God raised Him from the dead; and for many days He appeared to those who came up with Him from Galilee to Jerusalem, the very ones who are now His witnesses to the people. And we preach to you the good news of the promise made to the fathers, that God has fulfilled this promise to our children in that He raised up Jesus, as it is also written in the second Psalm, “YOU ARE MY SON; TODAY I HAVE BEGOTTEN YOU”” As for the fact that He raised Him up from the dead, no longer to return to decay, He has spoken in this way: “I WILL GIVE YOU THE HOLY and SURE blessings OF DAVID.”
Here we discover that Psalm 2:7 was a prophecy that Jesus would return to life. That is, He would be resurrected. He was “begotten” or was “brought forth” (notice that is an acceptable meaning of the Hebrew word) from the grave. The root Greek word is GINOMAI and the tense of the word used here is a perfect active meaning that it is completed action in the past and had continuing effect to the time Acts 13:33 was written. That is, Jesus’ resurrection was so certain that it was spoken of as already having occurred. Hebrews 1:5 and 5:5 do not provide the explanation of Psalm 2:7 that is given in Acts 13:33 but merely quote Psalm 2:7. Only Acts 13:33 provides the explanation. Also note that GINOMAI is translated as “begotten” only four times in the New Testament: Acts 13:33; Philemon 10, Hebrews 1:5 and 5:5. So there are two key Greek words that are sometimes translated as “begotten” in the New Testament. This can be confusing, and it is a cause of error for those in many cults.
In summary, Jesus is referred to as the “one and only” Son and as the “Son of God.” That is He is our God who was begotten or resurrected from the grave. God bless.