In the Bhagavad Gītā, Kṛṣṇa explains the reason for his avatāras. In that discussion, he says that whenever dharma is in decline and adharma is ascendant, he will incarnate on earth to restore dharma.
So we can see that God has now become very personally involved with humanity—far different from the conception of Brahman in the Upaniṣads.
When incarnated on earth, God thus experiences life like humans do—with suffering, and travail, and so forth.
Although endowed with superior qualities, Rāma, for example, nonetheless exemplifies the humanness of God on earth.