Indeed, why not! We have an absurd number of software job openings now, both on the Starlink network side and the flight software / simulation side. Bonus points if you have a top secret clearance.

https://www.spacex.com/careers, category "software development".

I imagine ChuckMcM's reasons may be similar to my own: when last I checked, SpaceX didn't have any positions open for Bay Area residents unwilling to relocate.

But I do see on the careers page there's now a (single) Palo Alto based Software Engineer position open.

Intriguing!

Well there are a couple of reasons one might not, but the biggest one is that given people with a wide range of experience in both individual contributor and management roles it is often difficult to figure out how to match the skillset with the role. Send me an email (profile has it) and I'll send you a resume you can dump into the ATS system to see if anyone thinks I'd be a good fit. (And no, I don't send my resume to head hunters to shop around).

The second challenge is that I am in a position to be reasonably frank when the biggest threat one can hold over me is to be fired. I have found that some managers don't appreciate employees for whom their "hire/fire power" over them doesn't give them any leverage. This combined with a general perception that I am a good manager, means that I tend to develop a followship whether or not I'm in a leadership role. This can lead to "issues" no matter how hard I try to prevent them.

There's some jobs in there that are absolutely my dream job. But unfortunately, I probably can't due to ITAR requirements, I'm not from the U.S.

Or does the "eligible to obtain the required authorizations from the U.S. Department of State" apply?

It is possible to get ITAR authorization without being a US citizen or permanent resident. However, it is a long and arduous process, and even then those employees are restricted from some information. For that reason, it probably won't be considered unless you are very highly qualified.

If I were you, I'd read up on ITAR qualification and, if you think you would be eligible and are highly qualified, just apply.