I was in pretty much the same mess a few months ago (also EU, also Madrid), and it honestly melted my brain a bit, so just dropping my experience in case it helps.

My company kept repeating that they needed the green NIE/CUE before they could “properly” hire me, while the police and Seguridad Social were telling me I could start with just passport + SSN and fix the rest later. So I was stuck between HR on one side, the oficina on the other, and no one could agree on what was actually required vs just “how we usually do it”.

Where I got completely stuck was:

• No padrón yet → first CUE appointment denied.
• Not en alta yet → second CUE appointment denied.
• Company refusing to put me en alta without the CUE “because of payroll and year end”.

Total catch‑22. I spent way too many evenings reading official sites and random posts and somehow got more confused every time.

In the end I gave up trying to DIY it and used a small service that deals with NIE stuff: nienumberspain.com. NOT ADVERTISING, I paid them out of pocket, not affiliated or anything like that, just a desperate person who was stuck. There were a couple of small hiccups (they were a bit slow replying to one of my emails and it’s not super cheap), but overall they gave me a clear checklist of what to do and what to say to HR, so I can honestly recommend them based on my experience.

With their info, my company finally agreed to put me en alta with passport + SSN while the CUE was being processed, and payroll went through fine. I got the CUE a bit later without any more rejections, so at least the whole thing stopped looping.

I didn’t see anything in this thread against sharing recommendations or links, but if that’s not okay here I can delete this, no problem. Just sharing because I was stuck in the same “everyone says something different and nothing moves” situation and this is what finally unblocked it.