Correct. Whoever believes, "believe" being the qualifier, has been born of God. Belief here is prior to being born of God. Sure sounds like a "new birth" here, Brother Luke.
It IS the new birth and it takes place BEFORE faith in that verse.
Whoever BELIEVES (presently) HAS BEEN (in the past) born of God.
Whoever is eating HAS BEEN sitting at the table. That sentence tells us that sitting at the table PRECEDED eating.
Look back a page.
I John 2:29 If ye know that he is righteous, ye know that every one that doeth righteousness is (in the Greek literally HAS BEEN) born of him.
Is John saying that one is doing righteousness BEFORE he was born of God here? NO! NOBODY denies that.
This is the EXACT same language used by the EXACT same author only a FEW paragraphs earlier.
One more time literally just a handful of sentences earlier.
I John 4:7 Beloved, let us love one another: for love is of God; and every one that loveth is (in the Greek literally HAS BEEN) born of God, and knoweth God.
Which comes first there, Willis? Loving or being born of God??
Being born of God of course! NOBODY reputable argues otherwise.
So in I John 5:1 John is saying that just like the new birth precedes righteousness in 2:29 and just like the new birth precedes loving in 4:7 the new birth precedes faith in 5:1.
Everyone who believes that Jesus is the Christ has been born of God...