Single crystal paleointensity (SCP) reveals that the Moon lacked a long-lived core dynamo, though mysteries remain. An episodic dynamo, seemingly recorded by some Apollo basalts, is temporally and energetically problematic. We evaluate this enigma through study of ~3.7 billion-year-old (Ga) Apollo basalts 70035 and 75035. Whole rock analyses show unrealistically high nominal magnetizations, whereas SCP indicate null fields, illustrating that the former do not record an episodic dynamo. However, deep crustal magnetic anomalies might record an early lunar dynamo. SCP studies of 3.97 Ga Apollo breccia 61016 and 4.36 Ga ferroan anorthosite 60025 also yield null values, constraining any core dynamo to the Moons first 140 million years. These findings suggest that traces of Earths Hadean atmosphere, transferred to the Moon lacking a magnetosphere, could be trapped in the buried lunar regolith, presenting an exceptional target for future exploration.