Next step up is EMT training.
It is hard to get into these courses in some states due to the ride-along requirements. I, too, just wanted to do the classroom; but having to be associated with an EMS squad made it a non-player.
It's more likely that the military teaches effective first aid.
Back a million years ago when I was in the Air Force in Alaska, we had our aircraft maintenance ancillary training dudes go to the Army base and take the "Combat First-Aid" course. They loved it. They did saline IM injections. We incorporated many of the things they learned.