How can a US corporation hire startup employees in Germany?

As ypu already pointed out the answer to your question mainly depends on the business strategy. There are many aspects to thought of. The following shall give an overview on some main points:
Setting up the German GmbH seems to be the right way in the means of a long term perspective.
The German corporation is an own legal person with own liabilities and tax obligations. Therefore this construction would (with a few exceptions) avoid the liability of the US parent. And from a tax point of view there could be some opportunities for tax planning.
On the other hand establishing the German GmbH Comes along with a couple of formal and organizational obligations. The Company Needs to be set up by notarial deed and needs a share capital of at least EUR 25.000,00 (which has to be paid in at least in half). Furthermore you would need a director who is responsible for all activities, especially preparing and filing the annual financial statements (Jahresabschluss) at due date and fulfilling all tax and other public obligations.
Also a question of the long term strategy is if you want to hire "real" employees or only instruct freelancers. In Germany you will find strict labour laws protecting the employees, especially if the Company grows up to more than ten employees. Freelancers on the other hand can be handled more freely but probably won't identify as much with their tasks. And additionally, if they are working nearly exclusively for you in the eyes of labour law a freelancer easily can be qualified as employees, too.
As you can see, the main questions is how strongly the US parent wants to commit itself to the German or European expansion. To get some more detailed advise which road to take, we strongly recommend to consult a lawyer or business advisor who can point out the pending risks and possibilities individually.