how long does it take for the depo shot to work?

Specifically for when you are post partum. I tried to ask this one time before but I got horrible answers that didn't even answer my question. Do not try to lecture me on whether I should get it or not. Do not try to tell me that I have have to wait 6 weeks regardless. That is not the case for every mom. Plenty of doctors give their patients the go ahead to have sex at 5,4 even 3 weeks postpartum. I'm asking this question because my doctor forgot to give me my depo shot at discharge and I'm weighing my options right now. I'm possibly going to schedule to get a different birth control method depending on the answers I get. I tried to google it but found nothing that answered my question.