That being said, I am seriously thinking about setting up my company in another country with a more appealing legal entity structure. Either the US or Estonia (EU E-Residency). Appreciate your advice here as well!
Concerning LLC be careful that there are double taxation treaties and that you first find an accountant who specialises in running a LLC from Ger/Aut. Otherwise you’ll pay twice in tax + high fees for the extra paperwork the accountant needs to do locally.
I personally had a look at having a UK Ltd run from Austria, there are plenty of companies specialising in that (just google UK Ltd Österreich/Deutschland). Not sure to what extent that’s still possible post Brexit.
All in all, especially if the big company is willing to pay upfront, I would personally go for a GmbH, might be more expensive to set up but saves you troubles in the long term I think.
Having said that, I’m only a programmer myself, please don’t rely on my advice here, definitely talk to a local accountant about that, they usually have a free consultation to get started.
If I were you I'd go ahead and establish the LLC, and then just see if the client wants to move forward. If they do, there's no shame of hiring a few contractors on to help you get to where you want to get to. If they don't, then you still want an LLC
I have an LLC, and I'm well aware that I'll probably never make a dime on my side project. I just have no interest in commingling my personal and business finances.
Overall I'd definitely go for it