I think God does punish in some way, although punishment sounds like a harsh & heavy word. Chastises should be the right term.
Hebrews 12:5-8
And you have forgotten the exhortation which speaks unto you as unto children, My son, despise not the chastening of the Lord, nor faint when you are rebuked of him:
For whom the Lord loves he chastens, and scourges every son whom he receives.
If you endure chastening, God deals with you as with sons; for what son is he whom the father chastens not?
But if you be without chastisement, of which all are partakers, then are you illegitimate children, and not sons.