> However, with evidence from the rock record of a dynamo for the past 3.5-4.2+ billion years, this leaves a long gap where it is more difficult to explain what drove the geodynamo.

Dynamo theory also suggests that the Earth has had a dynamo since its formation (in the impact process that formed the Moon). The reason being is that one can argue that in the present day the Earths dynamo is subcritical which essentially means it can maintain a strong field but not magnetize the core from a weak magnetization state. If this is correct and Earths dynamo is subcritical now then it is almost certainly subcritical throughout its life (since it was more rotationally constrained in the past, faster rotation) and so the dynamo must have existed since the formation of the Moon.