Won't address SpaceX though I know people there, but I too used to be on a track with an emphasis on individual accomplishment (academic mathematician) -- a lot about single-handed delivery. Sometime in my late 30s I realized that unfortunately, haha, the most impactful accomplishments are team efforts. To do big work, I realized I should find the right team. I am still working out what this means for my own career, but it's a huge change in mindset. And I'm working at a large, old-ish corporation now, and I think we are slowly & painfully changing how something very practical gets done.
I guess what I'm trying to say is that if you want to actually change the world, you're unlikely to do actually do it at a tech startup. You're instead likely to talk a lot about it while the real world-changing things are happening elsewhere. But you'll probably be happier at the startup because you get more of that magic combination of autonomy, teamwork, and quickly tangible results. I just personally get frustrated that almost every startup and its employees act like they're working on the biggest problems in the world when they just... aren't.
Edit: forgot to mention. I know two people who left ULA for similar reasons to you and went to SpaceX. They loved working at SpaceX in comparison to ULA because the level of company ambition, speed, and impact was so ridiculously higher. However, one of them left SpaceX to go to a smaller aerospace startup and the other is now at Raytheon for the superior work-life balance. I'm not sure what the lesson is there...