I suspect the indwelling Holy Spirit enables such love.
Begotten of God/born of God/born from above/born of the Spirit, I'm not convinced it's the same as 'indwelling', but no doubt the source for this agape is the regenerate heart, and it comes NATURALLY:
14 (for when Gentiles that have not the law
do by nature the things of the law, these, not having the law, are the law unto themselves;
15 in that
they show the work of the law written in their hearts, their conscience bearing witness therewith, and their thoughts one with another accusing or else excusing
them); Ro 2
So naturally does this agape come to the heavenly born that they may not even be aware of acting on it:
37 Then shall the righteous answer him, saying, Lord,
when saw we thee hungry, and fed thee? or athirst, and gave thee drink?
38 And
when saw we thee a stranger, and took thee in? or naked, and clothed thee?
39 And
when saw we thee sick, or in prison, and came unto thee? Mt 25
It's as if they weren't even conscious of doing anything out of the ordinary, like doing these things came to them 'naturally', from the heart, like Paul articulated, "when Gentiles that have not the law do by nature the things of the law...they show the work of the law written in their hearts"
Like the Samaritan:
33 But a certain Samaritan, as he journeyed, came where he was: and when he saw him,
he was moved with compassion, Lu 10
Agape comes naturally to the heavenly born.