God has no children, or brothers, sisters, cousins, aunts or uncles. There is just One God, creator of the Heavens and of the Earth. Pagan mythologies often have multiple gods with family members, but God, that is YHWH, is Israel's only God. Gentiles can have however many they fancy. One may sometimes say figuratively that we are all God's children, and there's nothing wrong with that. But if one talks about specific children, separate from the rest of humanity, than one is a polygamist and most likely a pagan.
Of course he could have. And actually I am one of his many children. The keyword, is "begotten". Gods Spirit overshadowed Mary & she became preggers. Christ alone, out of all that God had formed or created was worthy. God knows what's best.