Advaita is not atheism. Īśvara — the Lord, the personal God — is fully real at the empirical level. The relationship between the personal God and the absolute Brahman is one of the most subtle points in Advaita philosophy.
The God who creates the universe, who sustains it, who dissolves it at the end of a cosmic cycle — this is Īśvara, the Lord. In the Advaita framework, Īśvara is fully real. Prayers reach Īśvara. Devotion to Īśvara purifies the mind. Īśvara's grace is real and operative. This is not a concession or a compromise. It is the Advaita account of what the personal God is.
But Advaita adds something that other Vedanta schools do not: Īśvara is Brahman viewed through the limiting adjunct of māyā. Not that Brahman has become Īśvara by some transformation — Brahman is unchanging and does not become anything. But Brahman, when the inquiry approaches it through the categories of causation (who created this?), relationship (who sustains this?), and devotion (who do I surrender to?), appears as the personal, all-knowing, all-powerful Lord who is the source and support of the universe.
Remove the lens of māyā — which the inquiry does, progressively — and Brahman is seen as it is: nirguṇa (without attributes), not a creator who stands apart from creation, not a being who relates to other beings, not the God of any particular tradition. Pure consciousness, without boundaries, without properties that can be enumerated.
Advaita's position is not that Īśvara does not exist. It is that Brahman exists more ultimately than Īśvara — that Īśvara is the highest reality available within the empirical framework, and Brahman is the reality in which the empirical framework itself appears.
The Advaita distinction between Saguṇa Brahman (Brahman with attributes = Īśvara) and Nirguṇa Brahman (Brahman without attributes = the absolute) is one of Rāmānuja's primary targets in his Viśiṣṭādvaita critique. Rāmānuja argues: if Nirguṇa Brahman is the higher reality, and Saguṇa Brahman/Īśvara is Brahman-through-māyā, then Īśvara is lower than the absolute. This makes Īśvara a penultimate reality — and worship of Īśvara a means but not an end. Rāmānuja finds this theologically unacceptable: Brahman with attributes (Viṣṇu/Nārāyaṇa) is the highest reality, and the attribution of properties to him is not a limitation but a perfection.
Śaṅkara's response: the attributes of Īśvara are not limitations in the pejorative sense. They are upādhis — limiting adjuncts that allow Brahman to appear as the creator, sustainer, and lord. Within the empirical frame, Īśvara's attributes (omniscience, omnipotence, compassion) are real and operative. The point is not that these attributes are somehow less than real, but that Brahman's nature is not exhausted by any set of attributes, however exalted. The absolute is the inexhaustible ground from which Īśvara, with all attributes, appears.
The Māṇḍūkya Upaniṣad 1.6 describes Turīya as Īśāna sarvasyādhipatiḥ — the Lord, the ruler of all. This creates an identity: Turīya = Brahman = Īśvara. But Turīya is also described as niṣprapañca — without phenomenal appearance, without causal relationship to the world. The apparent contradiction — Turīya is both the Lord (relational, causal) and without phenomenal appearance (non-relational, non-causal) — is the Māṇḍūkya's compressed statement of the two-level doctrine. At the pāramārthika level, Turīya/Brahman has no causal relationship to anything (because there is nothing other than Brahman to be related to). At the vyāvahārika level, the same Brahman appears as the causal Īśvara. Both descriptions are simultaneously valid at their respective levels.