Cross-trained Firefighter/EMTs or Firefighter/Paramedics are about 60 years old now. Prior to the 1960s, "EMS" as we know it wasn't really a think in the United States. There was essentially no emergent medical care rendered in the prehospital environment. Patients were picked up and transported to the hospital either by the funeral homes in hearses or by the police in paddy wagons. Nothing was done for them en route.
Emergent prehospital medical care started in several places in the United States in the late 1960s and early 1970s. Most notably, Pittsburgh, Miami, and Los Angeles County. In Pittsburgh, a physician trained a crew of Black men to be among the first Paramedics in the country and founded the "Freedom House" ambulance service. These people were trained to start IVs, administer medications, treat trauma, and so on in the Black neighborhoods of Pittsburgh that were underserved by existing emergency services. They did such a great job that even the White people started asking for Freedom House to respond because they knew that was the only way that they would get medical care. At the same time the Los Angeles County Fire Department, under the direction of an Emergency Department physician, trained a small number of Firefighters as Paramedics and had them initiate medical treatment at the scene of an emergency. This was popularized by the TV show "Emergency!". Simultaneously, Dr. Eugene Nagel cross-trained firefighters from the Miami-Dade Fire Department as Paramedics and experienced positive results.
After "Emergency!" raised awareness to the effectiveness of actual EMS services, they rapidly spread across the country. Each state developed and regulated its EMS services a little bit differently. In places out west, it was popular for the fire departments to run EMS in its entirety as no other service wanted the responsibility. In North Carolina, EMS was regulated to the counties which is why there are a lot of county-run EMS services here. Regardless, across the country it was soon realized that fire departments were very well positioned to respond to medical calls because the fire stations and personnel were already deployed so that they could get anywhere in their jurisdiction within about 5 minutes. So, firefighters were cross-trained as EMTs and Paramedics and medical equipment was added to the trucks. Nowadays, in municipal and suburban departments approximately 50-70% of the call volume for fire departments is for medical emergencies. The firefighters typically arrive on scene first and can assess, treat, and stabilize the patients. When the ambulance arrives, care is transferred and for critical patients the firefighters can ride in to the hospital to assist with patient care or drive the ambulance to the hospital so that both EMS crew members can be in the back with the patient.