When is the right time to challenge the Paramedic exam as an MD?

I’m in my last year of medical school, getting ready to apply for EM residency. My biggest regret in this process is not going to medic school before medical school. I still volunteer in my free time as a basic for a local ambulance agency, however I would like to be able to expand my scope. I have heard of other MDs challenging the NREMT paramedic exam, however I’m curious when would be the right time to do that. For instance should I do it shortly after I graduate with my MD or wait until I complete my EM residency? Or if anyone has experience working with an MD who got there medic without going to medic school, am I being naive to think I could/should do this.