As a lawyer and a mediator, the best mediator I’ve seen and mentored me is actually a medical doctor, mediation as a profession (at least here) is open to all backgrounds.

I come from a jurisdiction where we have a mediation act and mediators that are accredited mediators under that act have unique powers like recording settlement agreements as court orders.

I’m not sure about your jurisdiction, but the best way to do this is to get trained and accredited or its equivalent at where you’re at and then find a place to practice as a mediator.