The only entities that can enforce GDPR are the DPAs in various EU countries. So if some action is taken against a non-EU company, it's anyway done by one of the DPAs - e.g. if there's a complaint against some USA company by a German citizen, it would be the German DPA handling that.

Any decisions of German DPA can be contested just as any other administrative decisions in German courts, the German DPA is fully under their authority. Yes, you won't have your local courts, but it doesn't mean that you can't appeal - you simply have to file this appeal where the contested decision was made.

You get the courts that the person you're servicing uses. Like when you sell to someone in a particular country and have to abide by their sales and tax laws.