Hello and welcome!
An EJ20 turbo? From an Impreza? You may very well blow up a little engine like that, which is why it doesn't get done.
Of course if you are set on it it can be done (nearly anything can be done with enough money thrown at it). You will need to strengthen everything about the engine to be able to withstand the extra forces being applied. This will mean pistons, rods and various other bits being replaced with forged parts. Possibly the entire block being replaced.
The exhaust will need replacing with a unit that can house the turbo and all the bits around it will need strengthening.
The ECU will need to be replaced to one that can control your fueling and turbo pressure.
The wiring looms will need to be replaced to match that.
The fuel pump will also need attention so the injectors are able to get enough fuel.
The injectors will need an upgrade otherwise they won't be able to squirt enough fuel in to keep up with the extra air being forced in.
There will be more.....
And once you have spent thousands (and it will be thousands) of £'s getting that extra power from the fully forged engine you will need to work on the drive train. The gearbox may well be able to contain the extra torque but will the clutch?
You'll need to upgrade the brakes and suspension as well or you won't be able to go around corners. Or stop.
And after all that you won't see massive BHP/torque gains
Don't get me wrong, I'm all for people modifying their cars, just be sure you know what you are letting yourself in for. Once you start on this route you can kiss goodbye to your bank balance
You may want to start with a different car.