Hello and welcome.
Yes, it's possible to add a turbo. Anything is with enough money.
I'm just gonna copy/paste a post I made earlier today....
Does your car have a turbo model? If so that makes it a little easier to source parts.
Start here -->
https://www.torquecars.com/tuning/adding-turbo.php
A few things to consider with turbos:
Engine strengthening - more power is more pressure and you don't want to blow up your block. This involves rods, pins, head, gaskets, nearly everything.
Injectors - more air needs more fuel in the chamber.
Fuel pump and lines - get that fuel to the injectors.
Exhaust manifold and pipes - get the gas out and spinning the turbo wheel.
ECU remap - if your OE can be remapped then happy days, else you'll need a piggy back ECU to control boost, fuelling, timing etc.
This is not going to be cheap. To give you an idea check out Mighty Car Mods on YouTube. This recent video gives a cost of fitting a turbo to a Yaris