Does your car have the sensors for remote operation mounted inside somewhere? Not sure where they are from the factory, but perhaps the interior light or in the front pillar region and near the rear window ... I thought key/fob remote was standard on GTI's in which case you'd just need the fob and a suitable key blade to cut and code.
If you know someone with VagCom, they could scan the car and check whether the module for remote central locking is present and functioning.
Best Wishes.
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