I would ask the SM or another BSA resource but I'm not directly involved in my family members BSA experience so I pose my question here for you knowledgeable folk. For my own edification CAN (not should) a brand new Boy Scout earn a merit badge(s) prior to earning the rank of Scout?
Reading the handbook and any online resources I would say that technically it is allowed. I see no restrictions on when a merit badge can be earned. However at a personal level I would argue that it is more important for the new Scout to focus on the initial ranks and acclimating to the overall scout experience first.