That meshes well with another study that found that children under 5 assume adults know everything that the child knows. It's only after around age 5 that children begin to stop ascribing that trait to adults. Link:

Lane concludes: "…data from the current study provide compelling evidence that when children begin to understand the cognitive limitations of humans, they typically attribute those same limitations to God, and this applies even to religiously exposed children.

Only later, at around age 5 years did religiously exposed children reliably differentiate between humans’ fallible mental abilities and inaccurate mental states versus God’s less fallible abilities and states.

These results suggest that in their everyday reasoning, even children who are raised in religious settings often initially understand God’s mind as constrained and fallible, very similar to their understanding of ordinary human minds."

So children have to develop an understanding of omniscience, even if they are raised in a religious environment. However, when raised in a religious environment, they seem to understand omniscience earlier - evidence of the importance of learning, as well as brain maturation.