Does the Qur’an assume that its readers have already heard of “Allah”?
No the Qu’ran does not assume anything, Allah does not assume anything, Allah knows. Allah is actually clearing up misconceptions of the false beliefs people had of Allah at that time, Allah is telling us about his characteristics and making it much clearer for us who he (swt) is so that we have a much better understanding and are therefore able to reach him more easily.