This is a verse that has been well debated not only among Greek Scholars (and the vast majority of them side against what is seemingly your proposition - that this verse states being born again 'causes' faith/belief) as well as here in the BB,
Here is an exert from John of Japan speaking directly to and with Archangle of this very passage:
Thus IOW - John (writing 1 John) is simply saying that the person who believes in Jesus gives evidence of being born of God, yet this is without any reference to when this being born of God actually took place. This is supported by the surrounding passages as well as context of the book which is speaking to - believers who were already in and of the faith.
I think that verse really means love one another.