Yes, it could be a non-profit. But, the application process to become a non-profit can be quite lengthy. However, one option would be to get another non-profit to sponsor you. You would basically work as a department or division of an existing non-profit until your application comes through. You could approach a city government, church, etc ... someone else in the area that's already a non-profit.

On the other hand, who really cares if it's a non-profit? You mention that it might "sound better." But, there is really no reason to advertise this fact.