Not sure where you're located, but in the US most ambulances aren't based out of hospitals, usually there's ambulance stations, or they're attached to a fire company.

Now it's a big country with a lot of different types of towns with their own unique situations, but there's a lot of cases where your local ambulance company is going to be a lot closer to you than a hospital, which means they can make up the difference pretty easily with their sirens , and you start getting at least some level of treatment from EMTs or paramedics that much sooner.