Short answer? No.
Between your car payment, which will be high since you won't be getting a great rate with little to no credit, and your insurance payment, which will be high due to being a new driver with a sporty car, you won't have enough money to fill the tank with the premium gas a wrx requires once a week (for the average driver.) Not to mention other maintenance costs associated with car ownership (fluids, tires, repair of a performance car that is nearly a decade old)
On top of the concrete numbers that say you can't afford it, I don't think a WRX is a good car for a kid learning to drive. You WILL want to drive it fast/race your friends, you WILL encounter unexpected maintenance costs and I can nearly guarantee you WILL get into at least one accident.
Moral of the story, if you want a car so you can stare at it sitting in the driveway get a WRX.
If you want a car to actually drive and go places in, get a more sensible first car like a Civic or Corolla.