Is it possible to install a turocharger onto a non-turbo 2008 Mazda 3 hatchback?

I have a 2008 Mazda 3 hatchback, that year of the car has a few variants that can have a turbo installed in it from the factory. I bought it used and the previous owner did some very small modifications to it (air intake, exhaust, speakers, mechanic said everything was kosher). The car runs well but I was wondering partially out of curiosity and party because it would be nice to have a turbo in there tuned primarily for fuel economy like some newer model cars have. So my question is, can an aftermarket turbo be installed into a Mazda 3, if it is the factory variant that didn't come with a turbo? I am not a car guy, I would take it to a shop to have it installed by professionals who know what they are doing, I just want to know if said modification is even possible as I know the two engines are slightly different.
Not sure if it is the s Touring or Grand Touring, can't find it in the owners manual.