In another part of my business life, I have an advisory connection to business brining another European aviation company to the US, working on FAA certification.
As I understand it, in theory there is an agreement between Europe and the US that type certificates should be a check the boxes paperwork exercise as they are supposed to recognize each others certifications, though in reality lots of politicking and lobbying in the background to get through the process, though the wheels turn slowly....
Though I am confident there are many here for more suitably positioned to comment!