American Company Spinning-up an office in Europe

Having a tax nexus in another country simplifies the hiring process, letting the company avoid contractors if they wish. It’s nicer for said employees as they don’t have to handle all aspects of employment as a contractor (or hire such help).

It’s some degree of hassle for the company, but if they need or want expat staff it might be the better approach.

Might help to add what you're trying to get from the expansion. Also where existing staff is located, as coordinating schedules goes from mildly annoying on the east coast to materially difficult on the west coast.

There are people / companies that will do it for you: registration, office, recruitment.