We don’t.
Writing was invented in the range of 3300-3400BCE and the earliest coherent texts of any kind we have are from 2600BCE at the earliest. We only have archaeological evidence of anything that happened before that, and there’s nothing special about 4241BCE in that record. (The nature of archaeology makes dating prehistoric things with that level of precision risible anyway.)
But lunar cycles are 29.5 days, not 28.