We started at 7 months since we were certainly going to wait till 6 months and 7 seemed a-a bit funkier b-that's when my mother had me start.
Truth is, LO tried to grab food at around 4-5 months. She also tried to "eat" plastic bags and newspaper at that time so I figured her judgement was unreliable
You most certainly have the right to wait with a 4 month old baby. Sort of sad that your ped doesn't know WHO and APA recommendations.