Earlier quoted context omitted.
I think financially it might best to stick at Google but change jobs. However, since you mentioned Space-X, remember that your skills set is not the core of their technology so you would not be able to get into one of the critical teams immediately. But sometimes you can make multiple jumps in position with time till you get closer to what you desire. Use your friends and former coworkers to help you lead into new op…
I've wondered about getting a degree in aerospace...
What your comments about aerospace remind me of is something I would myself frequently do: fantasizing about a different industry about which I know very little. (Years ago, I used to imagine going back to school to study law, on the grounds that being a lawyer is a good way to really work for social change.)
Obviously I didn't go back to school, and I certainly can't tell you what the right decision for you is. I think a bit of curiosity about the road not taken is natural--but you also have to be clear-eyed about what the alternatives actually look like.
To your specific question, however, I would strongly recommend interviewing at a few other teams inside the company and a few other companies. Before I came to my current employer, I interviewed here and a few other places. Some of them struck me by how _bad_ the interviewers were; in fact, my interview experience at my current employer (where the interviewers impressed me by their intelligence) convinced me, at the time, that if I didn't get the job I would stay at my then-employer rather than move to a less impressive place.
So interviewing can be clarifying in terms of showing you what else is out there, and helping you make a trade-off between natural wanderlust and, you know, not settling for something shitty just because it's new. ;)